The line of the equation y=x+1 and the parabola of equation y=x^2-1 intersect at two points, P and Q.

Question

The line of the equation y=x+1 and the parabola of equation y=x^2-1 intersect at two points, P and Q. What are the coordinates of the midpoint M of the segment PQ?

Answer 1

The graphs intersect when x²-1 = x+1

 

                                        x² - x - 2 = 0

 

                                        (x-2)(x+1) = 0    x = 2 or x = -1

 

Points of intersection are P and Q where:

 

P = (2, 2+1) = (2,3)

Q = (-1, -1+1) = (-1, 0)

 

M = midpoint of PQ = ([2+(-1)]/2, [3+0]/2) = (1/2, 3/2)

 

 

Answer 2

y = x + 1

y = x² -1

 

x + 1 = x² - 1

0 = x² - x - 2

0 = (x - 2)(x + 1)

 

The two points are (2, 3) and (-1, 0)

 

You can find the midpoint.