M(x,y) is the midpoint of segment cd with endpoints c(5,9) and d(17,29)?

well to find the midpoint of any two points, you have to use the midpoint formula which is

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

so basically, you just take the average of the x and y coordinates of the two points

so the midpoint of this would be [(5+17)/2,(9+29)/2]=(22/2,38/2)=(11,19)

First find the midpoint M using the formula:

x=1/2(x2+x1)

and

y=1/2(y2+y1)

So solving first for the x-intercept:

x=1/2(x2+x1)

x=1/2(5+17) *note: x2 and x1 can also be 17 and 5.

x=11

Then Solving for the y-intercept:

y=1/2(y2+y1)

y=1/2(9+29) *note: y2 and y1 can also be 29 and 9 .

y=19

So the coordinates of the midpoints are 11 and 19

M(11,19)

Now proving mc=md, we use the distance formula.

Let us first solve for segment mc:

The distance formula is d=√(x2-x1)^2 + (y2-y1)^2 and in this case

line segment mc =√(x2-x1)^2 + (y2-y1)^2

Substitute the x and y coordinates of m and c into the equation:

mc=√(5-11)^2 + (9-19)^2

mc= 2√34

Now let us solve for line segment md:

Just like what we did above, substitute the x and y coordinates of m and d into the equation:

md=√(17-11)^2 + (29-19)^2

md=2√34

Since mc= 2√34 and md=2√34,

mc=md

(a.) M = ((5 + 17)/2, (29 + 9)/2) = (11, 19)

(b.) MC = √(5 - 11)² + (19 - 9)²)

MD = √(17 - 11)² + (10)²

Note that 17 - 11 and 5 - 11 are technically the same values when squared therefore MC = MD.