Answer:
The slope of NP is [tex]\frac{-5}{7}[/tex] ⇒ B
Step-by-step explanation:
- In any square, every two opposite sides are parallel and every two consecutive sides are perpendicular
- Parallel lines have the same slope
- The product of the slopes of the perpendicular lines is -1, which means if the slope of one m, then the slope of the other is [tex]\frac{-1}{m}[/tex] (reciprocal m and change its sign)
- The rule of the slope of the line which passes through the points (x1, y1) and (x2, y2) is m = [tex]\frac{y2-y1}{x2-x1}[/tex]
In square MNPR
∵ MN and NP are adjacent sides
∴ MN ⊥ NP
∵ M = (3, 8) and N = (-2, 1)
∴ x1 = 3 and y1 = 8
∴ x2 = -2 and y2 = 1
→ Use the rule of the slope above to find the slope of MN
∴ m(MN) = [tex]\frac{1-8}{-2-3}[/tex]
∴ m(MN) = [tex]\frac{-7}{-5}[/tex]
∴ m(MN) = [tex]\frac{7}{5}[/tex]
∵ MN ⊥ NP
∴ The product of their slopes = -1
→ Reciprocal the slope of MN and change its sign
∴ m(NP) = [tex]\frac{-5}{7}[/tex]
∴ The slope of NP is [tex]\frac{-5}{7}[/tex]
