A quadrilateral has vertices at (-2,1),(0,4),(5,2)and(1,-1).Do the diagonals have the same midpoint.Justify your answer.
Answers
If you do not like distance formula, no problem.
Calculate all the slopes of the lines containing the sides of the quadrilateral. If two opposite sides have the same slope, these sides are parallel. You should expect to have two pairs of the same slopes.
These two slopes are negative reciprocals, which means PQ is perpendicular to QR.
If slopes of next sides are negative inverses, then the adjacent sides (PQ and QR for example) are perpendicular. Follow the suggestion above, if the diagonals are perpendicular, (slopes again!), then the figure is a square.
Path: 2 pairs of parallel sides (parallelogram) → right angle (rectangle) → perpendicular diagonals (square).
Examples how to calculate slopes below:
PQ slope:
mPQ = (4-2)/(0-3)
= -2/3
mQR = (1-4)/(-2-0)
=3/2.
Answer:
plzz give me brainliest ans and plzzzz follow me
