Question

In quadrilateral PQRS, the coordinates are (0,0), R(a +c, b), and S(a, b). How can you use coordinate geometry to show that the diagonals are perpendicular

Answer 1

Answer:By definition, perpendicular line are two lines that intersect at right angles. In other words, the angle made by two lines should be 90°. Therefore, the use of distance formula does not help because it only tells you if the sides are equal. It does not tell you about the intercepted angle.

A technique that can help you to know if two straight lines are perpendicular is is you find their slopes. Let's say the slope of line 1 is m1 and the slope of line 2 is m2. If m1*m2 yields a product of -1, then the lines are perpendicular. This is because if m1 is the negative reciprocal of m2, the lines are perpendicular. But if m1=m2, the lines are parallel, meaning they don't intersect at all.

Therefore, the answer is: Find the slopes and show that their product is -1.

hope it help