Question

Rectangle TUVW is on a coordinate plane at T (a, b), U (a + 2, b + 2), V (a + 5, b − 1), and W (a + 3, b − 3). What is the slope of the line that is parallel to the line that contains side UV?

Answer 1

The slope of the line that is parallel to the line containing side UV of rectangle TUVW is -1, as parallel lines have identical slopes.

Step-by-step explanation:

The question asks for the slope of the line that is parallel to the line containing side UV of rectangle TUVW on a coordinate plane. To find the slope of a line segment between two points, we use the formula m = (y2 - y1) / (x2 - x1).

Here, UV connects the points U(a + 2, b + 2) and V(a + 5, b - 1).

Substituting these into the formula, we get the slope m of UV as follows:

• m = (b - 1 - (b + 2)) / (a + 5 - (a + 2))
• m = (b - 1 - b - 2) / (a + 5 - a - 2)
• m = (-3) / 3
• m = -1

Therefore, the slope of any line parallel to UV would also be -1, since parallel lines have equal slopes.