explain why a line is perpendicular to anotherone line is passing through (8,8) and (4,2) and other line is passing through (-1,5) and (-4,7) how can i prove perpendicularity?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The slope of perpendicular lines has a product of -1.

The slope of the line passing through (8,8) and (4,2) is

s = (8 - 2)/(8 - 4) = 6/4 = 3/2

The slope of the line passing through (-1,5) and (-4,7) is

s' = (7 - 5)/( -4 + 1)

=> 2 / -3

s*s' = (3/2)*(-2/3) = -1

This proves that the lines are perpendicular.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since the lines are given by the points they passing through, we'll use slopes of the lines to explain why they are perpendicular.

By definition, the product of the slopes of 2 perpndicular lines is -1.

Slope of line through the points  (8,8) and (4,2) is:

m1= (y2-y1)/(x2-x1)

x1=8,y1=8,x2=4,y2=2

m1 = (2-8)/(4-8)

m1 = -6/-4

m1 = 3/2

Now, we'll consider the next two points (-1,5) and (-4,7).

m2 = (7-5)/(-4+1)

m2 = -2/3

We'll calculate the product of the slopes:

m1*m2=-1

(3/2)*(-2/3) = -1

Therefore, the given lines are perpendicular.

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