Midpoint Exercises for the ACT
Instructions: Try the midpoint exercises below. Check your answers and the solutions in the next section.
1. What is the midpoint of a line that passes through the following points: (8, 3) and (4, 1)?
2. A straight line on a graph crosses through points (1, 2) and (3, 4). What is the midpoint of this line?
3. A line has a y-intercept of 5 and lies on point (8, -2). What is the midpoint between these two coordinates?
4. Find the midpoint of the graph of a line that lies on the following coordinates: (−4, 2) and (2,−4).
5. Find the midpoint of coordinate (5, 3) and the x-intercept of 8.
Answers to the Midpoint Exercises
1. The answer is (6, 2).
The line passes through points (8, 3) and (4, 1).
midpoint x = (x1 + x2) ÷ 2 and midpoint y = (y1 + y2) ÷ 2
midpoint x = (8 + 4) ÷ 2 and midpoint y = (3 + 1) ÷ 2
midpoint x = 12 ÷ 2 and midpoint y = 4 ÷ 2
midpoint x = 6 and midpoint y = 2
2. The answer is (2, 3).
The line crosses through points (1, 2) and (3, 4).
midpoint x = (x1 + x2) ÷ 2 and midpoint y = (y1 + y2) ÷ 2
midpoint x = (1 + 3) ÷ 2 and midpoint y = (2 + 4) ÷ 2
midpoint x = 4 ÷ 2 and midpoint y = 6 ÷ 2
midpoint x = 2 and midpoint y = 3
3. The answer is (4, 1.5)
A line has a y-intercept of 5 and lies on point (8, -2). The y-intercept can be represented as the coordinates (0, 5).
midpoint x = (x1 + x2) ÷ 2 and midpoint y = (y1 + y2) ÷ 2
midpoint x = (8 + 0) ÷ 2 and midpoint y = (-2 + 5) ÷ 2
midpoint x = 8 ÷ 2 and midpoint y = 3 ÷ 2
midpoint x = 4 and midpoint y = 1.5
4. The answer is (-1, -1).
The line lies on the coordinates (−4, 2) and (2,−4).
midpoint x = (x1 + x2) ÷ 2 and midpoint y = (y1 + y2) ÷ 2
midpoint x = (-4 + 2) ÷ 2 and midpoint y = (2 + -4) ÷ 2
midpoint x = -2 ÷ 2 and midpoint y = -2 ÷ 2
midpoint x = -1 and midpoint y = -1
5. The answer is (6.5, 1.5).
The line has point (5, 3) and the x-intercept of 8. The x-intercept can be represented as the coordinates (8, 0).
midpoint x = (x1 + x2) ÷ 2 and midpoint y = (y1 + y2) ÷ 2
midpoint x = (5 + 8) ÷ 2 and midpoint y = (3 + 0) ÷ 2
midpoint x = 13 ÷ 2 and midpoint y = 3 ÷ 2
midpoint x = 6.5 and midpoint y = 1.5
How to Calculate the Midpoint
You may be asked to calculate the midpoints of two points on a line on a two-dimensional graph.
In order to do so, you would take two points from the line and use the formulas provided below to find the midpoints.
midpoint x = (x1 + x2) ÷ 2
midpoint y = (y1 + y2) ÷ 2
Midpoints – Practical Problems
You may also need to use the midpoint formula in practical problems, like those involving points on a map.
These questions are an example of a practical application of the midpoint formula, and knowing this will help you with coordinate geometry problems on the exam.
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