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