Question

What is the most specific name for the figure?

C
A. Parallelogram
C. Square
B
D
A
A(a, -b)
B(-a, -b)
C(-2a, b)
D(0, b)
B. Rectangle
D. Rhombus

Answer 1

The given points form a quadrilateral. To determine the most specific name for this figure, we can analyze the slopes of the diagonals.

In a rhombus, the diagonals are perpendicular bisectors of each other. This means they cut each other at right angles (90 degrees) and each diagonal divides the rhombus into two congruent triangles.

Let's calculate the slopes of the diagonals AC and BD:

The slope of AC is (b - (-b)) / (-2a - a) = 2b / -3a = -2b/3a

The slope of BD is (b - (-b)) / (0 - (-a)) = 2b / a

Two lines are perpendicular if the product of their slopes is -1. So, let's check:

(-2b/3a) * (2b / a) = -4b² / 3a² ≠ -1

Therefore, the diagonals are not perpendicular, so the figure cannot be a rhombus.

Explanation:

Answer 2

parallelogram

Explanation:

It is slanted and has four sides.