Question

Point C is located at (1, 2) and point D is located at (−4, −2). Find the x value for the point that is 1 over 4 the distance from point C to point D.

-0.25

3.25

-3.75

1.25

Answer 1

The answer is -0.25, When I graphed it that what I got.

Answer 2

-0.25

Explanation:

Coordinates of C =
`(x_(1) ,y_(1) )=(1,2)`

Coordinates of D =
`(x_(2) ,y_(2) )=(-4,-2)`

Let Coordinates of A= (x,y)

Since A point is located 1/4 the distance from C to D

So the remaining distance from point A to D is 3/4

Thus the ratio of CA : AD = m:n=1:3

Now to find points of A we will use section formula i.e.

`x=(mx_(2)+nx_(1))/(m+n)`

`y=(my_(2)+ny_(1))/(m+n)`

Substituting the values:

`x=(1*-4+3*1)/(1+3)`

`x=(-1)/(4)`

`x=-0.25`

Thus Find the x value for the point that is 1 over 4 the distance from point C to point D is -0.25

Hence option a is correct