Question

question 5 (multiple choice worth 1 points) (04.02 mc) 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 tu? options: 1, -1, 2, -2

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates of T and U

Point \( T \) is \((a, b)\) and point \( U \) is \((a + 2, b + 2)\). Let \( x_1=a,y_1 = b,x_2=a + 2,y_2=b + 2 \).

Step3: Calculate the slope of TU

Substitute into the slope formula: \( m=\frac{(b + 2)-b}{(a + 2)-a}=\frac{2}{2}=1 \).

Step4: Determine slope of parallel line

Parallel lines have equal slopes, so the slope of the line parallel to TU is also 1.

Answer:

1