SAT Math Multiple Choice Practice Question 52: Answer and Explanation
Given that B is the midpoint of line segment AC, which of the following is not true?
A. The distance from A to C is 5 units.
B. Point C has coordinates (7, 3).
C. The distance from A to B is equal to the distance from B to C.
D. The line segment connecting A to B has the same slope as the line segment connecting B to C.
E. The slope of AC is positive.
Correct Answer: A
A. As always with this type of problem, go through each answer choice one at a time. Choice (A) requires the distance formula, but first you need to find the coordinates of point C. You could use a formula, but common sense works best. To get from A to B, move 2 spaces to the right and 3 spaces up. Because Choice (B) is the midpoint of AC, do the same thing to get from B to C. Starting from (5, 0), moving 2 spaces to the right and 3 spaces up puts you at (7, 3). To find the distance from A to C, use the formula for the distance between two points (distance = ). Plug in the numbers for points A and C:
, which doesn't equal 5. Because the question asks you for the statement that isn't true, you have your answer — Choice (A).
When you take the real SAT, you don't have to check every possibility if you're pretty sure about your answer. If you finish early, you can always go back and double-check.
Those of you who want to see why the other choices are wrong (and therefore true), keep reading. You discovered that Choice (B) is true as you worked through Choice (A). You may think you need to use the distance formula again to check Choice (C), but this answer is really just the definition of the midpoint; if B is the midpoint of AC, this statement must be true. If you really want to do the math, both distances are . Choice (D) sure looks li