Question

Points A(6, 4) & B(0, 4) are reflected in the origin to get A' & B' respectively. What is the geometrical name for the figure ABA'B'.

• A. Rectangle
• B. Square
• C. Parallelogram
• D. Rhombus

Answer 1

The correct option is C

Parallelogram

A' is reflection of A (6, 4) in the origin which is (-6, -4)

B' is reflection of B (0, 4) in the origin which is (0, -4)

We can see that

$AB=\sqrt{(6-0{)}^2+(4-4{)}^2}=6$

$A^{\prime }{B}^{\prime }=\sqrt{(-6-0{)}^2+{[-4-(-4\left)\right]}^2}=6$

$A{B}^{\prime }=\sqrt{(6-0{)}^2+{[4-(-4\left)\right]}^2}=\sqrt{36+64}=10$

$A^{\prime }B=\sqrt{(-6-0{)}^2+(-4-4{)}^2}=\sqrt{36+64}=10$

The opposite sides are equal and parallel - Hence it is a parallelogram.