The first thing we are going to do in this case is find the slope of the GH line.We have then:
m = (y2-y1) / (x2-x1)
Substituting values:
m = (- 2-1) / (2 - (- 4))
m = (- 3) / (6)
m = -1 / 2
Then, the generic equation of the line is:
y-yo = m (x-xo)
Since the lines are parallel, then the slope is the same
m = -1 / 2
The line passes through point J, that is:
(xo, yo) = (1, 3)
The equation of the line will then be:
y-3 = (- 1/2) (x-1)
Rewriting:
y-3 = (- 1/2) x + 1/2
y = (- 1/2) x + 1/2 + 3
y = (- 1/2) x + 7/2
The points that pass through this line are:
(-3, 5)
5 = (- 1/2) (- 3) +7/2
5 = 3/2 + 7/2
5 = 10/2
5 = 5
(3, 2)
2 = (- 1/2) (3) +7/2
2 = -3 / 2 + 7/2
2 = 4/2
2 = 2
(5, 1)
1 = (- 1/2) (5) +7/2
1 = -5 / 2 + 7/2
1 = 2/2
1 = 1
Answer:
(-3, 5)
(3, 2)
(5, 1)
