English Medium इयत्ता १० - CBSE Question Bank Solutions

If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.      

If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.  

\[A\left( 6, 1 \right) , B(8, 2) \text{ and }  C(9, 4)\] are three vertices of a parallelogram ABCD . If E is the mid-point  of DC , find the area of  \[∆\] ADE.

If  \[D\left( - \frac{1}{5}, \frac{5}{2} \right), E(7, 3) \text{ and }  F\left( \frac{7}{2}, \frac{7}{2} \right)\]  are the mid-points of sides of  \[∆ ABC\] ,  find the area of  \[∆ ABC\] .

Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.

Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.

If the centroid of the triangle formed by points P (a, b), Q(b, c) and R (c, a) is at the origin, what is the value of a + b + c?

 what is the value of  \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}\] .

Write the coordinates of a point on X-axis which is equidistant from the points (−3, 4) and (2, 5).

If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C \[\left( \frac{3}{2}, \frac{5}{2} \right)\] , find x, y.

Two vertices of a triangle have coordinates (−8, 7) and (9, 4) . If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?

Write the formula for the area of the triangle having its vertices at (x₁, y₁), (x2, y₂) and (x₃, y₃).