Question

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 1

the answer is C. (1,0)

Answer 2

1. Points M and N have coordinates (-4,0) and (4,2), respectively.

Then vector
`\overrightarrow{MN}=(4-(-4),2-0)=(8,2)` is perpendicular to the neede line.

2. Write the equation of line that passes through the point P(2,-4) and is perpendicular to vector
`\overrightarrow{MN}=(8,2):`

`8(x-2)+2(y+4)=0,\\8x-16+2y+8=0,\\8x+2y-8=0,\\4x+y-4=0.`

3. Find the point on x-axis, that lies on the perpendicular line.

When y=0, then 4x-4=0, x=1 and point (1,0) lies on perpendicular line.

Answer: correct choice is C.