Question

graph and label the quadrilateral with the given vertices. then determine the most precise name for the quadrilateral.

\\(a(-8,-2), b(-4,4), c(4,4), d(8,-2)\\)

choose the correct graph of abcd below.

what is the most precise name for the quadrilateral abcd?

a. the quadrilateral abcd is a trapezoid.
b. the quadrilateral abcd is a rhombus.
c. the quadrilateral abcd is a parallelogram.
d. the quadrilateral abcd is a square.
e. the quadrilateral abcd is a kite.
f. the quadrilateral abcd is an isosceles trapezoid.
g. the quadrilateral abcd is a rectangle.

Explanation:

Identify the correct graph of ABCD

$$
LATEXBLOCK0
$$

Comparing the given coordinates with the options:

• Graph A shows vertices at \(A(-8, -2)\), \(B(-4, 4)\), \(C(4, 4)\), and \(D(8, -2)\).
• Graph B shows a parallelogram.
• Graph C shows a rectangle.
• Graph D shows a trapezoid with different coordinates.

Therefore, Graph A is the correct representation.

Determine the most precise name for ABCD

$$
LATEXBLOCK1
$$

Since \(BC \parallel AD\) and \(AB
ot\parallel CD\), \(ABCD\) is a trapezoid.

To find if it is an isosceles trapezoid, calculate the lengths of the non-parallel sides:

$$
LATEXBLOCK2
$$

Since \(AB = CD\), the trapezoid is an isosceles trapezoid.

Answer:

Question 1

• (A) Graph A (Correct answer)
• (B) Graph B
• (C) Graph C
• (D) Graph D

Question 2

• (A) The quadrilateral ABCD is a trapezoid.
• (B) The quadrilateral ABCD is a rhombus.
• (C) The quadrilateral ABCD is a parallelogram.
• (D) The quadrilateral ABCD is a square.
• (E) The quadrilateral ABCD is a kite.
• (F) The quadrilateral ABCD is an isosceles trapezoid. (Correct answer)
• (G) The quadrilateral ABCD is a rectangle.