Question

1. of the 4 vertices of rectangle abcd are graphed below. where would the location of point d be?

a (2,1)
b (0,2)
c (2,0)
d (-2,2)

Explanation:

Step1: Identify known points

From the graph, let's assume the known vertices (let's say A, B, C). Let's suppose A is at (-2, 0) (from the x - axis near -2, y = 0), B is at (-2, 5) (vertical line x=-2, y = 5), and C is at (2, 5) (x = 2, y = 5). In a rectangle, opposite sides are equal and parallel, and adjacent sides are perpendicular. So, the x - coordinate of D should be the same as C's x - coordinate (2) and the y - coordinate should be the same as A's y - coordinate (0), or vice - versa based on the rectangle's properties.

Step2: Analyze rectangle properties

In a rectangle, the coordinates of the fourth vertex (D) can be found by using the fact that the vector from A to B should be the same as the vector from D to C, and the vector from B to C should be the same as the vector from A to D. If A(-2,0), B(-2,5), C(2,5), then the vector from B to C is (2 - (-2), 5 - 5)=(4,0), and the vector from A to D should also be (4,0). So, D = A+(4,0)=(-2 + 4,0 + 0)=(2,0). Also, checking the options, option C is (2,0).

Answer:

C. (2, 0)