Question

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

√(2b - 2a)² + (0 - 0)² = 2a - 2b. MN will be half of that. This is B. b - a.
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Hope this helps!

Answer 2

Answer: The correct option is (B) (b - a) units.

Step-by-step 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.