Coordinate Geometry — Class 10 Mathematics (Standard) PYQs

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

(a) Vertices of a right triangle $ABC$ with $\angle B=90^{\circ }$ are $A(3, 4), B(1, 1)$ and $C(-8, 7)$. Find the value of $\tan A$.
OR
(b) Using distance formula, prove that the points $A(2, 3), B(-7, 0)$ and $C(-1, 2)$ are collinear.

(a) A circle centered at $(2,1)$ passes through the points $A(5, 6)$ and $B(-3, K)$. Find the value(s) of $K$. Hence find length of chord $AB$.
OR
(b) Prove that the point P dividing the line segment joining the points $A(-1, 7)$ and $B(4, -3)$ in the ratio $3:2$, lies on the line $x - 3y = -1$. Also find length of $PA$ and $PB$.

In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1:2$. Find length $AD$.

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

The coordinates of the centre of a circle are $(2a, a - 7)$. Find the value(s) of $a$ if the circle passes through the point $(11,-9)$ and has diameter $10\sqrt{2}$ units.

Find the ratio in which the y-axis divides the line segment joining the points $(5,-6)$ and $(-1,-4)$. Also find the point of intersection.

The end points of a diameter of circle are $(2,4)$ and $(-3,-1)$. The length of its radius is :

Find the length of the median through the vertex B of $\Delta ABC$ with vertices $A(9, -2), B(-3, 7)$ and $C(-1, 10)$.

The coordinates of the end points of a diameter of a circle are $(5,-2)$ and $(5,2)$. The length of the radius of the circle is :