NCERT Solutions · Class 10 Mathematics Coordinate Geometry

Find the distance between the points $\displaystyle (0,0)$ and $\displaystyle (36, 15)$. Can you now find the distance between the two towns A and B discussed in Section 7.2.

Determine if the points $\displaystyle (1, 5)$, $\displaystyle (2, 3)$ and $\displaystyle (-2, -11)$ are collinear.

Check whether $\displaystyle (5, -2)$, $\displaystyle (6, 4)$ and $\displaystyle (7, -2)$ are the vertices of an isosceles triangle.

In a classroom, $\displaystyle 4$ friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, "Don't you think ABCD is a square?" Chameli disagrees. Using distance formula, find which of them is correct.

Find the point on the $\displaystyle x$-axis which is equidistant from $\displaystyle (2, -5)$ and $\displaystyle (-2, 9)$.

Find the values of $\displaystyle y$ for which the distance between the points P$\displaystyle (2, -3)$ and Q($\displaystyle 10$, y) is $\displaystyle 10$ units.

If $\displaystyle \mathrm{Q}(0,1)$ is equidistant from $\displaystyle \mathrm{P}(5,-3)$ and $\displaystyle \mathrm{R}(x, 6)$, find the values of $\displaystyle x$. Also find the distances QR and PR.

Find a relation between $\displaystyle x$ and $\displaystyle y$ such that the point $\displaystyle (x, y)$ is equidistant from the point $\displaystyle (3,6)$ and $\displaystyle (-3, 4)$.