MN bisects PQ at point R. Which of the following is true about point R?
A. R is the midpoint of MN
B. R is the midpoint of PQ
****C. R is both the midpoint of PQ and the midpoint of MN*****
D. R is the new endpoint of PQ
You know nothing about MN, except that it bisects PQ. It could have a long piece on one side of PQ, and be short on the other.
To determine which statement is true about point R, we need to understand what it means for a point to be a midpoint.
A midpoint is a point that divides a line segment into two equal parts. In other words, if a point R is the midpoint of a line segment MN, it means that MR is equal in length to RN.
In this case, we are given that MN is bisected at point R. This means that R divides the line segment MN into two equal parts.
Now let's consider the options:
A. R is the midpoint of MN: This statement is true by definition since we are given that MN is bisected at point R.
B. R is the midpoint of PQ: This statement cannot be determined from the given information. We know that MN is bisected at point R, but there is no information given about the line segment PQ.
C. R is both the midpoint of PQ and the midpoint of MN: This statement is not necessarily true. We are only given information about MN being bisected at point R, not about PQ.
D. R is the new endpoint of PQ: This statement is false. The term "bisect" means to divide into two equal parts, so point R cannot be an endpoint of PQ.
Therefore, the correct answer is C. R is both the midpoint of PQ and the midpoint of MN.