Question

Help! Will give medal!

Answer 1

i dont know but i will try

Answer 2

it is a party now

Answer 3

i think we need to use the midpoint formula

Answer 4

no not really, if i read it correctly you need to show they are parallel
compute the slope of both, you will find both have slope zero

Answer 5

so how would i get the answer?

Answer 6

since both points have the same y coordinate, they both have zero slope

Answer 7

\[(0,0),(x_2,0)\] slope is
\[\frac{0-0}{x_2-0}=0\]

Answer 8

\[\left(\frac{x_1}{2},\frac{y_1}{2}\right), \left(\frac{x_1+x_2}{2},\frac{y_1}{2}\right)\] compute the slope and it is still 0 since the numerator is the difference of the y coordinates

Answer 9

is that the proof that segment DE is parallel to segment AB?

Answer 10

?

Answer 11

Did you find the slope between points D and E ?

Answer 12

im not sure how to do that

Answer 13

they give complicated expression (i.e. not a simple number) for the x and y values of points D and E

but we can still use the formula to find the slope.

what is the y value of point E ?

Answer 14

y1/2

Answer 15

yes, and the y value of point D is the same thing, y1/2
now figure out "change in y", which means subtract
y1/2 - y1/2
any idea what that is ?

Answer 16

anything minus itself is zero

Answer 17

right

Answer 18

and thats point d?

Answer 19

we are doing point E's y - point D's y
in other words
y1/ 2 - y1/ 2

can you simplify that ?

Answer 20

0

Answer 21

change in y is 0

if we do change in x
x1 /2 + x2 /2 - x1 / 2 we get x2 /2 which is some number

the slope is change in y divided by change in x
0/some_number = 0

in other words the slope of DE is 0

that slope matches the slope of AB

therefore DE is parallel to AB

Answer 22

so that would be the answer?

Answer 23

yes