Question

question 11 (multiple choice worth 1 point) (04.02 mc) quadrilateral wxyz is on a coordinate plane. segment xy is on the line x - y = -3, and segment wz is on the line x - y = 1. which statement proves how segments xy and wz are related? o they have slopes that are opposite reciprocals of 1 and -1 and are, therefore, perpendicular. o they have the same slope of 1 and are, therefore, parallel. o they have slopes that are opposite reciprocals of 0 and undefined and are, therefore, perpendicular. o they have the same slope of -1 and are, therefore, parallel.

Explanation:

Step1: Rewrite line equations in slope - intercept form

The equation of a line in slope - intercept form is $y=mx + b$, where $m$ is the slope. For the line $x - y=-3$, we can rewrite it as $y=x + 3$, so the slope $m_1 = 1$. For the line $x - y = 1$, we rewrite it as $y=x - 1$, so the slope $m_2=1$.

Step2: Recall parallel and perpendicular slope rules

Parallel lines have the same slope. Perpendicular lines have slopes that are opposite reciprocals. Since $m_1 = m_2=1$, the segments on these lines are parallel.

Answer:

They have the same slope of 1 and are, therefore, parallel.