Answer:
the correct options are:
(–1, 3), (–2, 2) and (–5, –1)
Step-by-step explanation:
Given that a line passes through two points
A(-2, -4) and B(4, 2)
Another point P(0, 4)
To find:
Which points lie on the line that passes through P and is parallel to line AB ?
Solution:
First of all, let us the find the equation of the line which is parallel to AB and passes through point P.
Parallel lines have the same slope.
Slope of a line is given as:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![m=\dfrac{2-(-4)}{4-(-2)} = 1](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B2-%28-4%29%7D%7B4-%28-2%29%7D%20%3D%201)
Now, using slope intercept form (
) of a line, we can write the equation of line parallel to AB:
![y =(1)x+c \Rightarrow y = x+c](https://tex.z-dn.net/?f=y%20%3D%281%29x%2Bc%20%5CRightarrow%20y%20%3D%20x%2Bc)
Now, putting the point P(0,4) to find c:
![4 = 0 +c \Rightarrow c = 4](https://tex.z-dn.net/?f=4%20%3D%200%20%2Bc%20%5CRightarrow%20c%20%3D%204)
So, the equation is ![\bold{y=x+4}](https://tex.z-dn.net/?f=%5Cbold%7By%3Dx%2B4%7D)
So, the coordinates given in the options which have value of y coordinate equal to 4 greater than x coordinate will be true.
So, the correct options are:
(–1, 3), (–2, 2) and (–5, –1)