which is a similar idea.
Let’s try one:
14.In the xy-plane, which of the following is a point of intersection between the graphs of y =
x + 2 and y = x^2 + x − 2 ?
A) (0, –2)
B) (0, 2)
C) (1, 0)
D) (2, 4)Here’s How to Crack It
Think about what the question is asking: A point of intersection means a point that is on the graphs of
both equations. Therefore, the point would actually work if plugged into the equation of the line and the
equation of the parabola.
So, use PITA by testing the answer choices: Start with one of the answers in the middle and plug in the
point to each equation to see if it is true. The correct point of intersection will work in both functions. Try
(C) in the first equation: Does 0 = (1) + 2? No. So, (C) is not the answer. Try (D) in the first equation:
Does 4 = (2) + 2? Yes. So, try (D) in the second equation: Does 4 = (2)2 + 2 – 2? Yes. Because (D)
works in both equations, it is the correct answer.
Other Things You Can Do to a Line
The midpoint formula gives the midpoint of ST, with points S (x 1 , y 1 ) and T (x 2 , y 2 ). It’s simply the
average of the x-coordinates and the y-coordinates. In our example, the midpoint would be
.Let’s see an example of a midpoint problem.
2.In the xy-plane, what is the midpoint of the line segment with endpoints at (3, 4) and (0, 0)
?
A) (1.5, 2)
B) (5, 0)
C) (2.5, 0)
D) (3.5, 3.5)