Tip #17 to Get a Top ACT Math Score

You couldn't ask for easier points to boost your score. Every ACT has a midpoint and/or distance question. If you don't know the formulas, you don't stand much chance. But if you memorize them, right here and now, you will gain points, guaranteed! In fact, take a few minutes right now to cut out the flashcards from the back of this book. Bring them everywhere you go, school, sports, DMX concerts, parties, etc. Everyone loves math flash cards!

To find the midpoint between two points on a graph, use the midpoint formula. All this formula really says is, "Take halfway between the x numbers and halfway between the y numbers." Halfway between two numbers is the same as the average of the numbers, so the midpoint formula is like the average formula:

The distance formula also makes sense if you really look at it. It is based on the Pythagorean theorem (Skill 24). To find the distance between two points on a graph, use the formula

Cut out the flashcards at the end of this book to help you memorize these formulas.

Let's look at this question:

Solution: A midpoint is halfway between two points, really just the average. That's what the midpoint formula gives us, the average of the two points:

Correct answer: C

Example Problems

Easy

1. The endpoints of on the real number line are –14 and 2. What is the coordinate of the midpoint of ?
   1. –8
   2. –6
   3. –2
   4. 0
   5. 8
2. A line in the standard (x, y) coordinate plane contains the points M( –2, 4) and N(8, 10). What point is the midpoint of ?
   6. (–2, 4)
   7. (3, 3)
   8. (5, 3)
   10. (5, 7)
   11. (3, 7)

Medium

3. In the standard (x, y) coordinate plane, what is the distance between the points (–4, 2) and (1, –10) ?
   1. 3
   2. 5
   3. 9
   4. 11
   5. 13
4. A diameter of a circle has endpoints (–2, 10) and (6, –4) in the standard (x, y) coordinate plane. What point is the center of the circle?
   6. (2, 3)
   7. (4, 6)
   8. (6, 4)
   10. (12, 8)
   11. Cannot be determined from the given information

Hard

5. A city's restaurants are laid out on a map in the standard (x, y) coordinate plane. How long, in units, is the straight-line path between Paul & Elizabeth's restaurant at (17, 15) and The Green Bean restaurant at (12, 5) ?
   1. 
   2. 
   3. 
   4. 11
   5. 

Answers

1. B A midpoint is halfway between the two points, really just the average. That's what the midpoint formula gives us:
2. K A midpoint is halfway between the two points, really just the average. That's what the midpoint formula gives us:
3. E Use the distance formula:



4. F The center of the circle is in the middle of the diameter—the midpoint of the diameter. Midpoint
5. C This word problem is just asking for the distance between the two restaurants. Use the distance formula:

Go to: Tip #18