Coordinate Geometry

CBSE Class 10 · Mathematics · 50 past questions

These are the board's own papers. 235 more board questions reprinted in the books we use in class are for signed-in students: sign in.

Q1 2026

In the given figure, $\Delta$ ABC is an equilateral triangle. AD is a median of the triangle joining the… (with a figure)
Q2 2026

Diagonals AC and BD of square ABCD intersect at P. Coordinates of points B and D are (9, – 2) and (1, 6)… (with a figure)
Q3 2026

A point P(x, 7) divides a line segment joining the points A(- 5, 4) and B(7, 9) in a certain ratio. Find the…
Q4 2026

The line segment joining the points P(–4, –2) and Q(10, 4) is divided by y-axis in the ratio
Q5 2026

A circle centered at (2, 1) passes through the points A(5, 6) and B(−3, K). Find the value(s) of K. Hence…
Q6 2026

The distance between the points $(a\cos\theta+b\sin\theta,\,0)$ and $(0,\,a\sin\theta-b\cos\theta)$ is
Q7 2026 (Basic)

The distance between the points $(-4, 2)$ and $(1, 0)$ is…
Q8 2026 (Basic)

A (– 2, 3) and B (4, 1) are end points of the diameter of a semi-circle. The semi-circle intersects y-axis at…
Q9 2026 (Basic)

The vertices of a rhombus ABCD are A(−3, −4), B(5, −3), C(1, 4) and D(−7, 3). Find the length of both the…
Q10 Sample paper 2026-27

The point which lies on the perpendicular bisector of the line segment joining the points A $(-3, -4)$ and B…
Q11 Sample paper 2026-27

PM is a median of Δ PQR with vertices P $(5, -6)$, Q $(6, 4)$ and R $(0, 0)$. The length of PM is…
Q12 Sample paper 2026-27

Assertion-
Reason Based Questions…
Q13 Sample paper 2026-27

In what ratio does the x–axis divide the line segment joining the points (– 4, – 6) and (–1, 7)? Also, find…
Q14 2025

The coordinates of the end points of a diameter of a circle are $(5, -2)$ and $(5, 2)$. The length of the…
Q15 2025

The points ($-$5, 0), (5, 0) and (0, 4) are the vertices of a triangle which is a/an…
Q16 2025

The equation of a line parallel to the x-axis and at a distance of 3 units below x-axis is…
Q17 2025

If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and $x + y - 10 = 0$…
Q18 2025

The line represented by $\frac{x}{4} + \frac{y}{6} = 1$, intersects x-axis and y-axis respectively at P and…
Q19 2025

Two of the vertices of $\triangle$ PQR are P(−1, 5) and Q(5, 2). The coordinates of a point which divides PQ…
Q20 2025

AOBC is a rectangle whose three vertices are A(0, 2), O(0, 0) and B(4, 0). The square of the length of its…
Q21 2025

If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and $x + y - 10 = 0$…
Q22 2025

The mid-point of the line segment joining the points P($-4$, 5) and Q(4, 6) lies on…
Q23 2025

The coordinates of the centre of a circle are $(2a, a - 7)$. Find the value(s) of 'a' if the circle passes…
Q24 2025

Find the ratio in which the y-axis divides the line segment joining the points (5, – 6) and (– 1, – 4). Also…
Q25 2025 (Basic)

For a point $(3, -5)$, the value of (abscissa $-$ ordinate) is…
Q26 2025 (Basic)

The mid-point of a line segment divides the line segment in the ratio…
Q27 2024

Directions : Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two…
Q28 2024

Find the ratio in which the line segment joining the points (5, 3) and (–1, 6) is divided by Y-axis.
Q29 2024

Point P divides the line segment joining the points A(4, $-5$) and B(1, 2) in the ratio 5:2. Co-ordinates of…
Q30 2024

XOYZ is a rectangle with vertices X(–3, 0), O(0, 0), Y(0, 4) and Z(x, y). The length of its each diagonal is
Q31 2024

AD is a median of $\Delta$ABC with vertices A(5, – 6), B(6, 4) and C(0, 0). Length AD is equal to…
Q32 2024

If the distance between the points $(3, -5)$ and $(x, -5)$ is 15 units, then the values of $x$ are…
Q33 2024

The centre of a circle is at (2, 0). If one end of a diameter is at (6, 0), then the other end is at…
Q34 2024

Find the ratio in which the point $\left(\dfrac{8}{5}, y\right)$ divides the line segment joining the points…
Q35 2024 (Basic)

The mid-point of the line segment joining the points $(-1, 3)$ and $\left(8, \frac{3}{2}\right)$ is…
Q36 2024 (Basic)

The distance between the points $(2,-3)$ and $(-2,3)$ is…
Q37 2024 (Basic)

The diameter of a circle is of length 6 cm. If one end of the diameter is $(-4, 0)$, the other end on x-axis…
Q38 2024 (Basic)

Find the co-ordinates of the points of trisection of the line segment joining the points $(-2, 2)$ and…
Q39 2023

The coordinates of the vertex A of a rectangle ABCD whose three vertices are given as B(0, 0), C(3, 0) and…
Q40 2023

The area of the triangle formed by the line $\frac{x}{a}+\frac{y}{b}=1$ with the coordinate axes is…
Q41 2023

If Q(0, 1) is equidistant from P(5, – 3) and R(x, 6), find the values of x.
Q42 2023

The distance of the point (-1, 7) from x-axis is…
Q43 2023

The distance of the point (– 6, 8) from origin is…
Q44 2023

Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the… (with a figure)
Q45 2023

In what ratio, does $x$-axis divide the line segment joining the points A(3, 6) and B(–12, –3) ?
Q46 2023

The distance between the points $(0, 2\sqrt{5})$ and $(-2\sqrt{5}, 0)$ is
Q47 2023

In Question 19 and 20, an Assertion (A) statement is followed by a statement of Reason (R). Select the…
Q48 2023

If $(-5, 3)$ and $(5, 3)$ are two vertices of an equilateral triangle, then find co-ordinates of the third…
Q49 2023 (Basic)

The distance between the points $(3, 0)$ and $(0, -3)$ is
Q50 2023 (Basic)

Find the coordinates of the point which divides the line segment joining the points $(7, -1)$ and $(-3, 4)$…