Question

Find the value of k, if the point $(2,3)$ is equidistant from the points $A(k,1)$ and $B(7,k)$

• A. $k=17$
• B. $k=10$
• C. $k=13$
• D. $k=16$

Answer 1

The correct option is C $k=13$

Distance between two points $(x_1,y_1)$ and
$(x_2,y_2)$ can be calculated using the
formula $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$
Given, Distance between the points $(2,3);(k,1)=$ Distance between $ (2,3) ; (7,k) $

$\sqrt{{(k-2)}^2+{(1-3)}^2}=\sqrt{{(7-2)}^2+{(k-3)}^2}$

$=>{(k-2)}^2+4=25+{(k-3)}^2$

On expanding the squares and simplifying, we get $k=13$