decisionDetermine weather the line through (8,8) and (4,2) is perpendicular to the line through (-1,5) and (-4,7)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The slope of a line through the points (x1, y1) and (x2, y2) is given by m = (y2 - y1)/(x2 - x1). Two lines are perpendicular if the product of the slope is -1.

Here the slope of the line through (8,8) and (4,2) is: (8-2)/(8-4) = 6/4 = 3/2

That of the line through (-1,5) and (-4,7) is : (7-5)/(-4 + 1) = 2/-3

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

Therefore as the product of the slope is -1 , they are perpendicular.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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 know that the product of the values of the slopes is -1, then the lines are perpendicular:

m1*m2=-1

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

Therefore, the given lines are perpendicular.

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