Question

What's the equation of the line that's a perpendicular bisector of the segment connecting C (6, –12) and D (10, –8)? ANSWERS: A) y = –x – 2 B) y = x + 2 C) y = –1∕2x – 2 D) y = 2x – 6

Answer 1

Answer:

B) y = x + 2

Step-by-step explanation:

Coordinates of point C =$(x_1,y_1)=(6,-12)$

Coordinates of point D=$(x_2,y_2)=(10,-8)$

To find the equation of segment CD

Formula : $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Substitute the values in the formula :

$y-12=\frac{-8+12}{10-6}(x-6)$

y-12=x-6

y=x+6

When two lines are perpendicular to each other the product of their slopes is -1

Let the slope of perpendicular line be x

So, -1 \times x = -1

So, x =1

General equation : y = mx+c

So, Option B has slope = 1

So,the equation of the line that's a perpendicular bisector of the segment connecting C (6, –12) and D (10, –8) is  y = x + 2