Question

Given the points P(-3; 2), Q(2; 7) and R(-10; y). Determine the values of y if P is equidistant from Q and R.​

Answer 1

The values of y are 1 and 3

What is distance formula -

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

x1 and y1 are x and y coordinates of a point.

similarly x2 and y2 are x and y coordinates of another point.

Explanation with steps -

As point P is equidistant from Q and R, the distances PQ and PR should be the same.

So, calculate distance PQ can be calculated from the above formula

The distance PQ is $\sqrt{50}$

now use this distance to calculate the unkown 'y'

$\sqrt{50} =$ $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\sqrt{50} =$ $\sqrt{(-10-(-3))^2+(y-2)^2}$

$\sqrt{50} =$ $\sqrt{49+(y-2)^2}$

Squaring both sides

50 = 49 + $(y-2)^{2}$

$y^{2}-4y+3=0$

On factorizing,

$(y-1)(y-3)=0$

Thus we get values of y to be 1 or 3

To see more about distance formula

refer : https://brainly.com/question/1872885

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