Question

When the coordinates (2, 3), (4, 4), (6, 3), and (4, 2) are joined, which shape is formed?

Parallelogram

Rectangle

Rhombus

Square

Answer 1

A ( 2, 3 ); B ( 4, 4 ); C ( 6, 3 ) ; D ( 4, 2 )
AB² = ( 4 - 2 )² + ( 4 - 3 )² = 4 + 1 = 5
AB = √5
BC² = ( 6 - 4 )² + ( 3 - 4 )² = 4 + 1 = 5
BC = √5
Also: CD = √5 and DA = √5.
Answer: C ) Rhombus.

Answer 2

Equation of the line passing through (2, 3) and (4, 4) is given by y - 3 = (4 - 3)/(4 - 2)(x - 2)
y - 3 = 1/2(x - 2)
Equation of the line passing through (4, 4) and (6, 3) is given by y - 4 = (3 - 4)/(6 - 4)(x - 4)
y - 4 = -1/2(x - 4)


Therefore, the points form a rhombus.