Answer:
(2,0)
Step-by-step explanation:
For given line AB:
y-intercept = b = -2
slope = m = y₂-y₁/x₂-x₁
= -3/2-(-4) = -3/6 = -1/2
Equation of line AB:
y = (-1/2)x - 2
Finding equation of line that is parallel to line AB and passes through the point C(2,2):
Substituting the slope from line AB into the equation of the line
y = (-1/2)x + b.
Substituting the given point (-2,2) into the x and y values 2 = (-1/2)-2 + b.
Solving for b (the y-intercept)
, we get b = 1
Substitute this value for 'b' in the slope intercept form equation y = (-1/2)x + 1.
For x-intercept of the line, we let y = 0
0 = (-1/2)x + 1
x = -1(-2/1)
x = +2
So, the point on the x-axis that lies on the line that passes
through point C and is parallel to line AB is (2,0).
