Question

Which point on the x-axis lies on the line that passes through point C and is parallel to line AB?

(1, 0)
(0, 1)
(0, 2)
(2, 0)

Answer 1

(2,0)

Explanation:

Answer 2

Step 1

Find the slope of the line AB

Let

`A(-4,0)\ B(2,-3)`

we know that

The slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(-3-0)/(2+4)`

`m=(-3)/(6)`

`m=-(1)/(2)`

Step 2

Find the equation of the line

we know that

If two lines are parallel, then their slopes are the same

so

`m1=m2`

The equation of the line into slope-point form is equal to

`y-y1=m(x-x1)`

we have

`m=-(1)/(2)`

point
`C(-2,2)`

substitute

`y-2=-(1)/(2)(x+2)`

`y=-(1)/(2)x+1`

Step 3

Find the point on the x-axis that lies on the line

the equation of the line is
`y=-(1)/(2)x+1`

we know that

if the point lies on the x-axis

then

the y-coordinate of the point is equal to zero

so

For
`y=0`

find the x-value

`0=-(1)/(2)x+1`

`(1)/(2)x=1`

`x=2`

therefore

the answer is

the point is
`(2,0)`