Question

Prove that P (1,7), Q (4,2), R(-1, -1), S (-4, 4) are vertices of a square. Find the
slopes of its parallel sides & write your conclusion.​

Answer 1

A square does not have any parallel sides.

JUST TAKE OUT THE DISTANCE BY USING THE FORMULA AND IF THEY ARE EQUAL THEN THEY ARE THE SIDES OF A SQUARE..

HOPE THIS HELPS. . . .

Answer 2

For the points P (1,7), Q (4,2), R(-1, -1), S (-4, 4) to be the vertices of a triangle , the distance between any two consecutive vertices should be same.

Distance PQ = √(9+25) = √34

Distance QR = √(25+9) = √34

Distance RS = √(9+25) = √34

Distance SP = √(25+9) = √34

As all the distance PQ , QR , RS and SP are equal , so the given points are the vertices of a square.

Slope of the side PQ = (2-7)/(4-1) = -5/3

Slope of the side QR = (-1-2)/(-1-4) = 3/5

Slope of the side RS = (4+1)/(-4+1) = -5/3

Slope of the side SP = (4-7)/(-4-1) = 3/5

The side PQ, RS are parallel and the sides QR , SP are parallel.

The parallel sides have equal slopes.