Answer:
Yes, the lines are perpendicular because the product of their slopes equals -1 ⇒ B
Step-by-step explanation:
The product of the slopes of the perpendicular lines is -1
So to prove that the lines are perpendicular let us find their slopes
The rule of the slope is:
[tex]m=\frac{y2-y1}{x2-x1}[/tex] , where (x1, y1) and (x2, y2) are two points on the line
∵ Line M passes through points (2, -5) and (4, -3)
∴ x1 = 2 and x2 = 4
∴ y1 = -5 and y2 = -3
→ By using the rule of the slope above
∴ [tex]m=\frac{-3-(-5)}{4-2}=\frac{-3+5}{2}=\frac{2}{2}[/tex]
∴ The slope of line M is 1
∵ Line N passes through points (-4, -8) and (-6, -6)
∴ x1 = -4 and x2 = -6
∴ y1 = -8 and y2 = -6
→ By using the rule of the slope above
∴ [tex]m=\frac{-6-(-8)}{-6-(-4)}=\frac{-6+8}{-6+4}=\frac{2}{-2}[/tex]
∴ The slope of line N is -1
∵ 1 × -1 = -1
∴ The product of the slopes of lines M and N is -1
∴ Lines M and N are perpendicular
∴ Yes, the lines are perpendicular because the product of their
slopes equals -1.
