Question

P is the point on the y-axis which is equidistant from A(-5,-2) and B(3, 2), then PA = ___ cm.

• A. 2
• B. 6
• C. 3
• D. 5

Answer 1

The correct option is D 5

Given, A(-5, -2), B(3, 2).
Let, the coordinates of P be (0, y)
We have,
PA = PB
$\Rightarrow P{A}^2=P{B}^2\Rightarrow (-5-0{)}^2+(-2-y{)}^2=(3-0{)}^2+(2-y{)}^2\Rightarrow 25+4+y^2+4y=9+4+y^2-4y\Rightarrow 8y=-16\Rightarrow y=-2$

Therefore coordinates of P is (0, -2)

$\text{PA}=\sqrt{(-5-0{)}^2+(-2+2{)}^2}=\sqrt{25}=5cm$