Question

ABC has vertices A(1,5), B(9,7),and C (7.13). M is the midpoint of AB. And N is the midpoint of BC. Which of the following is the length of MN? A. 3 B. 4 C. 5 D. 6

Answer 1

your answer is c.5
you should this method

Answer 2

The right answer is C.5

This problem is illustrated in the Figure bellow. The problem asks for the length of the line in green. According to geometry, the midpoint formula of the line segment that joins the two points:

`(x_(1),y_(1)) \ and \ (x_(2),y_(2)) \ is \\ given \ by \ the \ following \ Midpoint \ Formula:\\ \\ Midpoint=((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2))`

So, for A and B:

`M=Midpoint=((x_(1)+x_(2))/(2),(y_(1)+y_(2))/(2)) \\ \\ M=((1+9)/(2),(5+7)/(2)) \\ \\ \therefore \boxed{M(5,6)}`

For B and C:

`N=((9+7)/(2),(7+13)/(2)) \\ \\ \therefore \boxed{N(8,10)}`

Finally, the length of MN can be found by using the distance formula:

`d=\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2} \\ \\ d=√((5-8)^2+(6-10)^2) \\ \\ d=5 \\ \\ \\ \boxed{Length \ of \ MN=d=5}`