Question

(1) What is the slope of the line containing the midpoint of the segment with endpoints at (2, 4) and (0, -2) and the midpoint of the segment with endpoints at (5, 1) and (1, 5)? Express your answer in simplest form.

(2) The lines -2x + y = k and 0.5x + y = 14 intersect when x = -8.4. What is the value of k?

Thank you!

Answer 1

1) To find the x of the midpoint, add the x values of the endpoints, then divide by 2
To find the y of the midpoint, add the yx values of the endpoints, then divide by 2
for the 1st segment, the x of the midpoint is (-2+0)/2 = -1
the y of the midpoint is (-2+4)/2 = 1
So the midpoint of the first segment is (-1,1)

now find the midpoint of the second segment in the same way.
Now that you have the 2 points, find the slope (assuming you know how to do that)

2. sub x = -8.4 into 0.5x + y = 14 and solve for y
You now have the intersection point.
sub that point into the first equation to find k