Question

One line passes through the point (-7,4) and (5,-4). Another line passes through points (-7,-4) and (2,2). Tell whether the two lines are :

A) Parallel
B) Perpendicular
C) Neither
D) Insufficient information

Answer 1

C

Step-by-step explanation:

calculate the slopes m of the 2 lines using the slope formula , then

• If the slopes are equal , then the lines are parallel

• If the product of the slopes is - 1 , then the lines are perpendicular

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )` ← slope formula

let (x₁, y₁ ) = (- 7, 4 ) and (x₂, y₂ ) = (5, - 4 )

substitute these values into the formula for m

m =
`(-4-4)/(5-(-7))` =
`(-8)/(5+7)` =
`(-8)/(12)` = -
`(2)/(3)`

repeat with (x₁, y₁ ) = (- 7, - 4 ) and (x₂, y₂ ) = (2, 2 )

m =
`(2-(-4))/(2-(-7))` =
`(2+4)/(2+7)` =
`(6)/(9)` =
`(2)/(3)`

Since slopes are not equal then the lines are not parallel

since -
`(2)/(3)` ×
`(2)/(3)` ≠ - 1, then the lines are not perpendicular

Answer 2

The lines with slopes -2/3 and 2/3 are perpendicular to each other because their slopes are negative reciprocals of each other. The answer is B) Perpendicular.

Step-by-step explanation:

To determine if the two lines are parallel, perpendicular, or neither, we need to calculate the slope of each line. The slope (m) is calculated by the formula:

m = (y2 - y1) / (x2 - x1)

For the first line, which passes through points (-7,4) and (5,-4), the slope is:

m1 = (-4 - 4) / (5 - (-7)) = -8 / 12 = -2/3

For the second line, which passes through points (-7,-4) and (2,2), the slope is:

m2 = (2 - (-4)) / (2 - (-7)) = 6 / 9 = 2/3

Now, let's compare the slopes:

• If two lines are parallel, their slopes are equal.
• If two lines are perpendicular, the product of their slopes is -1.
• Otherwise, the lines are neither parallel nor perpendicular.

In this case, since m1 = -2/3 and m2 = 2/3, and these slopes are negative reciprocals of each other, this means the lines are perpendicular to each other. Therefore, the answer is B) Perpendicular.