Coordinate Geometry Tests — Pick a Level and Start
Tap a level to see every test in it. Level 1 is set at real SSC CGL difficulty — start there the day you finish the formulas. Level 2 is pitched above the exam, to push accuracy under pressure.
Level 1 SSC CGL Level Checking… View tests
Same difficulty as the real SSC CGL paper — one formula applied cleanly. Quadrants and distances from the axes; reflections in the axes, the origin, x = a, y = b and y = x; the distance and midpoint formulas; internal and external division and the ratio cut by an axis; the centroid, circumcentre, orthocentre and incentre; collinearity; the area of a triangle or quadrilateral from its vertices; intercepts and the triangle a line makes with the axes; slopes and every form of a line; parallel and perpendicular lines; unique, no and infinitely many solutions; perpendicular distance and the gap between parallel lines; and the equation of a circle. A steady score here means the chapter is exam-ready.
Level 2 Above SSC CGL Level Checking… View tests
Harder than the exam asks, because every question chains two steps or runs one backwards. A point fixed by its quadrant and a ratio of distances; an endpoint from nested midpoints; the gap between two division points; the orthocentre from the centroid and circumcentre; a right angle hidden in three vertices; a rhombus whose third corner sits on an axis; a centroid lying on a given line; a quadratic in k tested against the constants; a median’s y-intercept; the axis points of a perpendicular bisector; a circle’s chord on the y-axis; and a disc wedged between two parallel lines. Clear these and the real paper feels easy.
A coordinate geometry question is a formula waiting to be applied to numbers. Once you know which object the question is about — a point, a segment, a line, a triangle or a circle — the working is usually two or three lines. The skill is turning the words into the right formula: equidistant means the perpendicular bisector, dividing a segment means the section formula, never meeting means equal slopes, and a line touching a circle means its distance from the centre equals the radius.
The marks are lost in three places. The first is sign slips — subtracting a negative coordinate, or reading the y-intercept of 4x − 3y = 24 as 8 instead of −8. The second is mixing up the centres: the centroid comes from the sum of the vertices divided by 3, the circumcentre is the same distance from all three, and in a right triangle the orthocentre is the right-angle vertex. The third is keeping one answer when the condition gives two — a given distance or area usually produces two values of k, and the question’s condition decides which one stays. Each test puts twenty-five coordinate geometry questions in front of you in one sitting, which is what makes those checks automatic.
How Many Coordinate Geometry Questions Are Asked in SSC CGL?
Coordinate geometry is a small but steady part of advanced maths. Tier I usually has none or one question and Tier II has one or two, most of them on intercepts, areas from vertices, slopes and the consistency of two linear equations.
| Chapter | Tier I (out of 25) | Tier II Paper I (out of 30) |
|---|---|---|
| Coordinate Geometry (points, lines, circles) | 0–1 | 1–2 |
| Geometry (triangles, quadrilaterals, circles) | 2–3 | 3–5 |
Counts vary by shift. The centroid, circumcentre and incentre work the same way in both chapters, so coordinate geometry is best prepared right after geometry.
What You Will Practice in the Coordinate Geometry Chapter
Points, distance and division
- Quadrants, signs and the distance of a point from each axis
- Reflections in the axes, the origin, the lines x = a and y = b, and the lines y = x and y = −x
- The distance formula — perimeters, equidistant points, and telling right, isosceles and equilateral triangles or squares and rhombuses apart
- The midpoint formula and the fourth vertex of a parallelogram
- Internal and external division, trisection points, and the ratio in which an axis or a line cuts a segment
Triangles and areas
- The centroid, circumcentre, orthocentre and incentre, and the Euler-line link H = 3G − 2O
- Collinearity by equal slopes or zero area
- The area of a triangle from its vertices, and the triangle joining the midpoints of the sides
- Quadrilaterals and polygons by the shoelace method, and rhombuses from their diagonals
- Areas bounded by a line and the axes, and by two or three lines
Lines, pairs of lines and circles
- Slope, inclination and the angle between two lines
- Point-slope, two-point, slope-intercept and intercept forms of a line
- Lines parallel or perpendicular to a given line, and the altitudes, medians and perpendicular bisectors of a triangle
- Unique, no and infinitely many solutions of a pair of linear equations, and three concurrent lines
- Perpendicular distance, the gap between parallel lines, the foot of a perpendicular and the image of a point in a line
- Circles — the equation from a centre and radius, from a diameter, and the radius from a tangent line
Formulas worth memorising
| Situation | Formula |
|---|---|
| Distance between two points | √[(x2 − x1)² + (y2 − y1)²] |
| Section formula, m : n internally | ((mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)); externally, replace + by − |
| Centroid | ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3) |
| Area of a triangle | ½|x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)|; zero means collinear |
| Slope | (y2 − y1)/(x2 − x1) = tan θ; for ax + by + c = 0 it is −a/b |
| Parallel / perpendicular | m1 = m2 / m1m2 = −1 |
| Intercept form | x/a + y/b = 1; the triangle with the axes has area ½|ab| |
| Pair a1x + b1y = c1, a2x + b2y = c2 | a1/a2 ≠ b1/b2 one solution; a1/a2 = b1/b2 ≠ c1/c2 none; all three equal: infinitely many |
| Point to line | |ax1 + by1 + c| / √(a² + b²) |
| Two parallel lines | |c1 − c2| / √(a² + b²), after matching a and b |
| Circle | (x − h)² + (y − k)² = r²; x² + y² + 2gx + 2fy + c = 0 has centre (−g, −f) |
| Right triangle | circumcentre = midpoint of the hypotenuse; orthocentre = the right-angle vertex |
The distance, section and area rows cover most Tier I questions. For lines, the slope row and the pair-of-equations row answer almost everything else.
The three mistakes that cost the most marks
- Losing a minus sign. The y-intercept of 4x − 3y = 24 is −8, and subtracting A = (−3, 5) means adding 3. Write every substitution in brackets before simplifying.
- Using the wrong centre. The centroid comes from the sum of the vertices divided by 3; the circumcentre is the same distance from all three; the incentre weights each vertex by the opposite side. In a right triangle the circumcentre is the midpoint of the hypotenuse.
- Keeping one root when there are two. A distance, an area or a squared ratio usually gives two values. Check both against the question — “positive”, “third quadrant” or the constants’ ratio decides which one stays.
Solved Examples — SSC CGL Coordinate Geometry Questions
PA² = PB² gives (x − 3)² + 16 = (x − 7)² + 4; the x² terms cancel, leaving 8x = 28, so x = 3.5. Check: PA² = 0.25 + 16 = 16.25 and PB² = 12.25 + 4 = 16.25. Answer: (3.5, 0)= ½|x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)| = ½|1(3) + 4(1) + 7(−4)| = ½|−21|. The modulus removes the sign. Answer: 10.5 square unitsa1/a2 = b1/b2: 2/6 = 3/k, so k = 9. The constants give 7/5, not 1/3, so the lines are distinct rather than the same line. Answer: 9= |ax1 + by1 + c| / √(a² + b²) = |5 + 24 − 3| / 13 = 26/13. Answer: 2 unitsHow the Coordinate Geometry Chapter Tests Work
- 25 questions per test, with a full question palette — answered, skipped, marked for review, not visited.
- Five figure questions in every test, each with an original diagram shown beside the question.
- Optional 15-minute timer — with the clock to build exam speed, without it while you are still learning the chapter.
- Marking: +2 correct, −0.5 wrong, 0 unattempted — the same scheme as the real paper.
- Solutions, shortcut tricks and concept notes open after you submit, question by question.
- English and हिंदी, chosen at the start of every test.
- Free with a TrickySSC account — sign in once with Google or your mobile number, and every test is open to you.
How to Prepare Coordinate Geometry for SSC CGL
- Learn the formulas as a chain. Distance leads to equidistant points and circles; the section formula leads to midpoints, centroids and trisection points; slope leads to parallel, perpendicular and every line equation.
- Sketch the points first. A ten-second sketch on rough axes shows the quadrant, any right angle and the rough size of the answer before any formula.
- Bracket every negative coordinate. Most wrong options in this chapter come from a single sign slip, and brackets make that slip visible.
- Look for a right angle. If two sides are perpendicular, the circumcentre, orthocentre and area each come in one line.
- Use the intercept form for axis questions.
x/a + y/b = 1answers intercept, area-with-axes and equal-intercept questions directly. - Compare ratios for pairs of lines. Write
a1/a2,b1/b2andc1/c2side by side; the pattern tells you unique, none or infinitely many. - Keep both roots until the end. Then apply the question’s condition — quadrant, sign or position — to choose between them.
- Check with a second method. An area from the vertex formula can be checked with the box method, and the foot of a perpendicular must satisfy the line.
- Do Level 1 untimed, the same day you finish the theory. It is set at real SSC CGL difficulty; the aim is picking the right formula, not speed.
- Repeat Level 1 with the 15-minute clock on, then move to Level 2. After that, verify against a previous year paper and a full mock test under locked sectional timing.
All SSC CGL Chapter Wise Tests
Every chapter below has its own free Level 1 and Level 2 tests with full solutions.
Browse all 45 chapter tests — Maths (35) · Reasoning (10)
- Number System
- Rule of Divisibility
- Remainder Theorem
- Decimal & Fraction
- LCM & HCF
- Square & Cube Root
- Number Series (AP & GP)
- Power, Indices & Surds
- Algebraic Formula
- Algebraic Result
- Algebraic Expression & Identities
- Percentage
- Profit & Loss
- Discount & Marked Price
- Simple Interest
- Compound Interest
- Ratio & Proportion
- Partnership
- Average
- Problems on Ages
- Mixture & Alligation
- Time & Work
- Pipe and Cistern
- Time, Speed and Distance
- Quadratic Equation
- Boat and Stream
- Races
- Trigonometry
- Heights & Distances
- Geometry
- Mensuration
- Coordinate Geometry
- Probability
- Statistics
- Data Interpretation
- All Maths chapters →
SSC CGL निर्देशांक ज्यामिति (Coordinate Geometry) चैप्टर टेस्ट — हिंदी में
निर्देशांक ज्यामिति का हर प्रश्न शब्दों को सही सूत्र में बदलने का खेल है। पहले पहचानें कि प्रश्न किसके बारे में है — बिंदु, रेखाखंड, रेखा, त्रिभुज या वृत्त — फिर हल अक्सर दो-तीन पंक्तियों का होता है। जैसे बराबर दूरी का अर्थ है लम्ब समद्विभाजक, रेखाखंड को बाँटने का अर्थ है विभाजन सूत्र (SECTION FORMULA), कभी न मिलने का अर्थ है समान ढाल (SLOPE), और वृत्त को छूने वाली रेखा का अर्थ है केन्द्र से उसकी दूरी = त्रिज्या।
अंक तीन जगह कटते हैं। पहली: ऋण चिह्न की गलती — ऋणात्मक निर्देशांक घटाना या अंतःखंड (INTERCEPT) का चिह्न भूल जाना। दूसरी: केंद्रों को आपस में मिला देना — केन्द्रक (CENTROID) तीनों शीर्षों के निर्देशांकों के योग का एक-तिहाई है, परिकेन्द्र (CIRCUMCENTRE) तीनों शीर्षों से समान दूरी पर है, और समकोण त्रिभुज में लम्बकेन्द्र (ORTHOCENTRE) समकोण वाला शीर्ष है। तीसरी: दो में से एक मान छोड़ देना — दी गई दूरी या क्षेत्रफल से k के प्रायः दो मान आते हैं, और प्रश्न की शर्त तय करती है कि कौन-सा सही है।
TrickySSC पर इस अध्याय के सभी टेस्ट हिंदी में उपलब्ध हैं — प्रश्न, विकल्प, आकृतियाँ, विस्तृत हल और शॉर्टकट ट्रिक सब हिंदी में। दो स्तर हैं: लेवल 1 (SSC CGL के स्तर का) और लेवल 2 (SSC CGL से कठिन)। प्रत्येक टेस्ट में 25 प्रश्न, वैकल्पिक 15 मिनट का टाइमर और +2 / −0.5 की वही मार्किंग जो असली परीक्षा में होती है।