If the coordinates of a point on the y-axis which is equidistant from the points $(13, 2)$ and $(12, - 3)$ is $(p, q)$ , then find the value of $p + q$ .

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Solution

Let P(0, y) be the required point and the given points be A(12 , -3) and B (13 , 2) Then PA = PB (given)
$\sqrt{{(12 - 0)}^{2} + {(- 3 - y)}^{2}} = \sqrt{{(13 - 0)}^{2} + {(2 - y)}^{2}}$
$\Rightarrow \sqrt{144 + {(y + 3)}^{2}} = \sqrt{169 + {(2 - y)}^{2}}$
$\Rightarrow y = 2$
$∴$ The required point on Y-axis is (0, 2). ( hint: since x cordinates are equal to '0' on y-aixs)

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If the coordinates of a point on the y-axis which is equidistant from the points (13,2) and (12,−3) is (p,q), then find the value of p+q.

Let P(0, y) be the required point and the given points be A(12 , -3) and B (13 , 2) Then PA = PB (given)√(12−0)2+(−3−y)2=√(13−0)2+(2−y)2⇒√144+(y+3)2=√169+(2−y)2⇒y=2∴ The required point on Y-axis is (0, 2). ( hint: since x cordinates are equal to '0' on y-aixs)

If the coordinates of a point on the y-axis which is equidistant from the points $(13, 2)$ and $(12, - 3)$ is $(p, q)$ , then find the value of $p + q$ .