Question

determine if S could lie on the perpendicular bisector if QR with the given coordinates. Q (-5-, -1) R (3, 7) S (4, -2)





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Answer 1

Using the formula for the distance between the two points, it is found that:

Yes, S could lie on the perpendicular bisector QR.

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The distance between two points, $(x_1,y_1)$ and $(x_2,y_2)$ is given by:

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

• The endpoints are: Q(-5, -1), R(3, 7)

• Point S is (4,-2).

The distance of S to Q is:

$D = \sqrt{(4 - (-5))^2 + (-2 - (-1))^2} = \sqrt{82}$

The distance of S to R is:

$D = \sqrt{(4 - 3)^2 + (-2 - 7)^2} = \sqrt{82}$

Same distance, thus:

Yes, S could lie on the perpendicular bisector QR.

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