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

b - a

Step-by-step explanation:

Given M and N are midpoints, let's find the coordinates of the midpoints first. Then we can use that information to find the length

The midpoint formula is

( (x1 + x2)/2, (y1 + y2) / 2 )

So M = ( (2a + 2c)/2, (0 + 2d)/2 ) = (a + c, d)

And N = ( (2c + 2b)/2, (2d + 0)/2 ) = (c + b, d)

Because the y-coordinates are the same (d), the distance from M to N is,

final x-coordinate minus initial x-coordinate

x-coordinate of N minus x-coordinate of M

(c + b) - (a + c)

Distribute the negative and remove the parentheses

c + b - a - c

Group the cs together

c - c + b - a

Cancel out the cs

b - a