Question

PLEASE HELP

Answer 1

Answer:

m is parallel to n

Step-by-step explanation:

Calculate the slopes of m, n, p and q using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

• Parallel lines have equal slopes

• The product of the slopes of perpendicular lines = - 1

For line m

using (x₁, y₁ ) = (- 2, 7) and (x₂, y₂ ) = (3, 5) ← 2 points on the line

m = $\frac{5-7}{3+2}$ = - $\frac{2}{5}$

For line n

using (x₁, x₂ ) = (- 5, 0) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line

m = $\frac{-2-0}{0+5}$ = - $\frac{2}{5}$

For line p

using (x₁, y₁ ) = (6, 15) and (x₂, y₂ ) = (10, 5) ← 2 points on the line

m = $\frac{5-15}{10-6}$ = $\frac{-10}{4}$ = - $\frac{5}{2}$

For line q

using (x₁, y₁ ) = (6, 15) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = $\frac{0-15}{0-6}$ = $\frac{-15}{-6}$ = $\frac{5}{3}$

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Checking the list

m ≠ parallel to q ( slopes are not equal )

q ≠ perpendicular to n ( product of slopes ≠ - 1 )

n ≠ parallel to q ( slopes are not equal )

p ≠ perpendicular to m ( product of slopes ≠ - 1 )

m is parallel to n ( slopes are equal )

p ≠ perpendicular to q ( product of slopes ≠ - 1 )

Thus m is parallel to n ← only one from list

Answer 2

A is perpendicular to n
m is parallel to n