Question

select all the true statements.
a. p ⊥ q
b. q ⊥ n
c. m || n
d. p ⊥ m
e. m || q
f. n || q

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Calculate slope of line $m$

For two points on line $m$: $(-2,7)$ and $(3,5)$, $m_m=\frac{5 - 7}{3+2}=\frac{-2}{5}=-\frac{2}{5}$.

Step3: Calculate slope of line $n$

For two points on line $n$: $(-5,0)$ and $(0, - 2)$, $m_n=\frac{-2-0}{0 + 5}=-\frac{2}{5}$. Since $m_m=m_n$, $m\parallel n$.

Step4: Calculate slope of line $p$

For two points on line $p$: $(0,-4)$ and $(6,15)$, $m_p=\frac{15 + 4}{6-0}=\frac{19}{6}$.

Step5: Calculate slope of line $q$

For two points on line $q$: $(3,5)$ and $(10,5)$, $m_q=\frac{5 - 5}{10 - 3}=0$.

Step6: Check perpendicular and parallel relationships

• Two lines are perpendicular if $m_1\times m_2=-1$. Two lines are parallel if $m_1 = m_2$.
• $m_p\times m_q=\frac{19}{6}\times0 = 0

eq - 1$, so $p$ and $q$ are not perpendicular.

• $m_q\times m_n=0\times(-\frac{2}{5}) = 0

eq - 1$, so $q$ and $n$ are not perpendicular.

• $m_p\times m_m=\frac{19}{6}\times(-\frac{2}{5})=-\frac{19}{15}

eq - 1$, so $p$ and $m$ are not perpendicular.

• $m_m

eq m_q$, so $m$ and $q$ are not parallel.

• $m_n

eq m_q$, so $n$ and $q$ are not parallel.

Answer:

C. $m\parallel n$