Question

This question has two parts. First, answer Part A. Then, answer Part B.

Part A
ANALYZE PROBLEMS Draw a square ABCD with opposite vertices at A (2,-4) and C (10,4) on a separate sheet of paper.
a. Find the other two vertices of the square and label them B and D. Assume 8 is located in Quadrant I.
B
Part B
b. Show that AD | BC and AB || DC.
and D
The slopes of AB and DC are Select Choice so they are parallel to each other. The slopes of AD and BC are
Select Choice, so they are parallel to each other.
c. Show that the measure of each angle inside the square is equal to 90°.
Because the slope of AB is Select Choice and the slope of BC is Select Choice the lines are Select Choice to each other.
Therefore, they form a right angle, which measures Select Choice. The same logic applies to all of the sides.

Answer 1

To find the other vertices of the square, calculate the length of a side using the distance formula and then use the symmetry of the square. To show parallel sides, calculate the slopes and compare. Each angle in the square is 90°.

Step-by-step explanation:

Part A

To find the other two vertices of the square, we need to find the length of a side of the square. Using the distance formula, we can calculate the length of AC: √[(10-2)^2 + (4-(-4))^2] = √(64+64) = √128 = 8√2. Since the square is symmetric, the length of BD is also 8√2. Now, we can find the coordinates of B and D:

B = (10, 4+8√2) = (10, 4+8√2)

D = (2, -4-8√2) = (2, -4-8√2)

Part B

b. To show that AD is parallel to BC, we can calculate the slopes of AD and BC. The slope of AD is (∆y/∆x) = ((-4-4) / (2-10)) = -8/-8 = 1. The slope of BC is ((4-4-8√2) / (10-2)) = (-8√2 / 8) = -√2. Since the slopes are the same, AD || BC.

To show that AB is parallel to DC, we can calculate the slopes of AB and DC. The slope of AB is ((-4-4) / (2-10)) = -8/-8 = 1. The slope of DC is ((-4-(-4-8√2)) / (2-10)) = (-8√2 / -8) = √2. Since the slopes are the same, AB || DC.

c. Since AD || BC and AB || DC, the opposite sides of the square are parallel. Therefore, each angle inside the square is equal to 90°, making it a right angle.

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