Which line is perpendicular to the line that passes through the points (3, –7) and (6, –16) and goes through the point (12, 8)?

Question

Which line is perpendicular to the line that passes through the points (3, –7) and (6, –16) and goes through the point (12, 8)?

y = -3x + 44

y = x/3 + 12

y = -x/3 + 12

y = x/3 + 4

Answer 1

Hi Anna,

The slope of a line that is perpendicular to another line has a slope that is equal to the negative reciprocal of the given line. We can use the two points to find the slope of the given line first:

(Note: The equation of a line can be written in the following form: y = mx + b where m is the slope of the line and b is the y-intercept.)

Slope:

m = (y₂ - y₁) = (-16 - - 7) = -9 = -3

(x₂ - x₁) ( 6 - 3 ) 3

The slope of a perpendicular line would be the negative reciprocal of -3 OR 1/3.

Now we have the slope of the new line and we can use the point (12, 8) to determine the y-intercept, b:

y= mx + b

y = 1 • x + b

3

8 = 1 •12 + b

3

8 = 4 + b

8 - 4 = 4 + b - 4

4 = b

The equation of the perpendicular will be:

y = 1 x + 4

3

Answer 2

the slope of the given line is (-16 - -7)/(6- 3)

= (-9)/3

= -3

so the slope of the perpendicular line is 1/3

B = y - mx = 8 - (1/3)(12)

= 8 - 4

= 4

y = (1/3)x + 4