which point on the x - axis lies on the line that passes through point p and is perpendicular to line mn…
which point on the x - axis lies on the line that passes through point p and is perpendicular to line mn? (0,1) (0,4) (1,0) (4,0)
Answer
Explanation:
Step1: Find slope of line MN
Let (M(-4,0)) and (N(4,2)). Slope (m_{MN}=\frac{y_N - y_M}{x_N - x_M}=\frac{2 - 0}{4-(-4)}=\frac{2}{8}=\frac{1}{4}).
Step2: Find slope of perpendicular line
The slope of a line perpendicular to line (MN) is (m=-4) (since the product of slopes of perpendicular lines is - 1, (\frac{1}{4}\times m=-1)).
Step3: Assume point - slope form of perpendicular line
Let point (P(2,-4)). The point - slope form of a line is (y - y_1=m(x - x_1)), so the equation of the perpendicular line is (y+4=-4(x - 2)).
Step4: Find x - intercept
Set (y = 0) in the equation (y+4=-4(x - 2)). Then (0 + 4=-4(x - 2)), (4=-4x+8), (4x = 4), (x = 1).
Answer:
(1,0)