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

A. [tex]\(-2\)[/tex]
B. 2
C. [tex]\(-1\)[/tex]
D. 1



Answer :

GinnyAnswer
To find the slope of the line that is parallel to the line containing side UV of rectangle TUVW, we follow these steps:

1. Identify the coordinates of points [tex]\( U \)[/tex] and [tex]\( V \)[/tex]:
- [tex]\( U(a+2, b+2) \)[/tex]
- [tex]\( V(a+5, b-1) \)[/tex]

2. Calculate the slope of line [tex]\( UV \)[/tex]:
The formula for the slope of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Substitute the coordinates of points [tex]\( U \)[/tex] and [tex]\( V \)[/tex]:
[tex]\[ \text{slope}_{UV} = \frac{(b-1) - (b+2)}{(a+5) - (a+2)} \][/tex]

3. Simplify the expression:
[tex]\[ \text{slope}_{UV} = \frac{b - 1 - b - 2}{a + 5 - a - 2} = \frac{-3}{3} = -1 \][/tex]

4. Determine the slope of the line parallel to [tex]\( UV \)[/tex]:
The slope of any line parallel to another line is the same as the slope of the original line.

Therefore, the slope of the line that is parallel to the line containing side [tex]\( UV \)[/tex] is:
[tex]\[ \boxed{-1} \][/tex]

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