Question

SOMEONE HELP PLEASE

In the figure, M and N are midpoints of RT and ST. What is the length of MN?

a + b
b - a
2

Answer 1

i have this same question, can anyone answer it?

Answer 2

So the correct answer is option B- ( b - a )

Explanation:

Given that M and N are the mid-points of RT and ST.

We are to find the length of MN.

As shown in the figure,

the co-ordinates of the point T are (2c, 2d),

the co-ordinates of the point S are (2b, 0),

and

the co-ordinates of the point R are (2c, 2d).

Since M is the mid-point of TR, so the co-ordinates of M are

`\left((2c+2a)/(2),(2d+0)/(2)\right)`=(c+a,d).

Also, N is the mid-point of TS, the co-ordinates of N are

`\left((2c+2b)/(2),(2d+0)/(2)\right)`=c+b,d)(.

Therefore, the length of the line segment MN calculated using distance formula will be

MN=
`√((c+b-c-a)^2+(d-d)^2)=√((b-a)^2)`=b-a.

Thus, the required length of MN is (b - a) units.

Option (B) is correct.