Question

If the distance between the points (5, -2) and (1, a) is 5, find the values of a.

Answer 1

We know, the distance between $(x_1,y_1)and(x_2,y_2)$

is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

Here, the distance = 5 units, $x_1=5$, $x_2=1$, $y_1=-2$ and $y_2=a$

Therefore, 5 =$\sqrt{(1-5{)}^2+(a+2{)}^2}$

⟹ $25=16+(2+a{)}^2$

⟹ ($2+a{)}^2=25-16$

⟹ ($2+a{)}^2=9$

Taking square root, 2 + a = ±3

⟹ a = -2 ± 3

⟹ a = 1, -5