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:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{2-(-4)}{4-(-2)} = 1[/tex]
Now, using slope intercept form ([tex]y = mx+c[/tex]) of a line, we can write the equation of line parallel to AB:
[tex]y =(1)x+c \Rightarrow y = x+c[/tex]
Now, putting the point P(0,4) to find c:
[tex]4 = 0 +c \Rightarrow c = 4[/tex]
So, the equation is [tex]\bold{y=x+4}[/tex]
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)
