if the distance between the points (a,-5) and (2,7) is 13 units the value of a is - Maths - Coordinate Geometry

Question

if the distance between the points (a,-5) and (2,7) is 13 units
the value of a is

Vimala · Accepted Answer

The distance between the points $(2, 7)$ and $(a, - 5)$ is 13 units.

The formula for distance between two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is

$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

In our problem, d = 13 units, $(x_{1}, y_{1})$ = $(2, 7)$ and $(x_{2}, y_{2})$ = $(a, - 5)$ .

Thus, substituting all the values in the formula for distance, we have,

$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} d^{2} = {(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} 13^{2} = {(a - 2)}^{2} + {(- 5 - 7)}^{2} 169 = a^{2} - 4 a + 4 + 144 25 = a^{2} - 4 a + 4 a^{2} - 4 a + 4 - 25 = 0 a^{2} - 4 a - 21 = 0 a^{2} - 7 a + 3 a - 21 = 0 a (a - 7) + 3 (a - 7) = 0 (a - 7) (a + 3) = 0 a - 7 = 0 a + 3 = 0 T h a t i s a = 7, a = - 3$

if the distance between the points (a,-5) and (2,7) is 13 units the value of a is .................