Question

If the line through the point (-2,6) and (4,8) is perpendicular to the line through the point (8,12) and (X, 24), find the value of X.

Answer 1

If a line is perpendicular then
m1×m2=-1
Slope of line is y2-y1/x2-x1
8-6/(4-(-2))×24-12/X-8=-1
2/6×12/x-8=-1
1/3×12/x-8=-1
12/3(x-8)=-1
12/(3x-24)=-1
12=-3x+24
3x=12
x=4

Answer 2

The value of x is 4.

Given,

The line through the point (-2,6) and (4,8) is perpendicular to the line through the point (8,12) and (x, 24).

To Find,

The value of x.

Solution,

The product of slopes of two perpendicular lines is equal to -1

m₁xm₂ = -1

The formula for calculating the slope when the coordinates of two points are given is

Slope = (y₂-y₁)/(x₂-x₁)

The slope of the two lines will be

m₁ = (8-6)/(4+2) = 2/6 = 1/3

m₂ = (24-12)/(x-8) = 12/(x-8)

Now,

m₁xm₂ = -1

1/3x12/(x-8) = -1

4 = 8-x

x = 4

Hence, the value of x is 4.

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