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Line k contains the points (-9,4) and (9,-8) in the xy-coordinate plane. What are the two other points that lie on line k?

Line k contains the points (-9,4) and (9,-8) in the xy-coordinate plane. What are-example-1
User Pawelbial
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4 votes

Answer

D. (-3, 0) and (3, -4)

Step-by-step explanation

Let the coordinate of the points be A(-9, 4) and B(9, -8).

We shall look for the gradient m of line using

m = (y₂ - y₁)/(x₂ - x₁)

Substitute for x₁ = -9, y₁ = 4, x₂ = 9 and y₂ = -8

m = (-8 - 4)/(9 - -9) = -12/18 = -2/3

From option A - D given, only C and D would have the same gradient of -2/3 as line AB

To know the correct option, we shall look for the equation of the line AB, that is,

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

(y - 4)/(x - -9) = (-8 - 4)/(9 - -9)

(y -4)/(x + 9) = -12/18

(y - 4)/(x + 9) = -2/3 -----------*

Between option C and D, only D satisfies the equation *

That is, using (-3, 0), we have (0 - 4)/(-3 + 9) = -4/6 = -2/3

Also, using (3, -4), we have (-4 - 4)/(3 + 9) = -8/12 = -2/3

User Elita
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