Question

Determine and prove what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value.

A(24, −8), B(12, −17), C(3, −5), D(15, 4)

The shape is a .

The perimeter of ABCD is .

The area of ABCD is .

Answer 1

square; 60; 225.

Explanation:

1) using the vectors rules to calculate the lengths of the sides AB; BC; CD and AD. When AB=BC=CD=AD it means, the shape is a square of rhombus.

2) using the vectors rules to calculate the lengths of the diagonales AC and BD. When AC=BD it means, the shape is a square.

3) The perimeter of the square ABCD is 15*4=60.

4) The area of the square ABCD is 15*15=225.

All the details are in the attached picture; answers are marked with colour.