ABCD is a rectangle formed by the points A( -1, -1 ), B( -1, 4), C(5,4), D(5, -1).P,Q,R and S are the mid points of AB,BC,CD and DA respectively.Prove that PQRS is a rhombus.

Proved

Step-by-step explanation:

Given

Required

Prove that PQRS is a rhombus

P = midpoint of AB

So:

Q = midpoint of BC

R = midpoint of CD

S = midpoint of DA

So, we have:

To show that PQRS is a rhombus, the distance between PQ, QR, RS and SW must be equal.

Distance is calculated as:

For PQ

For QR

For RS

For SP

From the calculations above:

Hence: PQRS is a rhombus

(z)-intergers

Step-by-step explanation:

set of whole numbers negative or positive