Question

If the parallel sides of a trapezoid contained by the lines y = -x + 5 and y = -x - 9, what equation represents the line contained by the midsegment?

Answer 1

The gradient of the midsegment is equal to the gradient of the 2 parallel sides of the trapezoid.

Gradient of the 2 lines = -1
Therefore, Gradient of midsegment = -1 also.

To get the equation of the midsegment, u need the gradient and also coordinates of one point that lies in this midsegment. This point will be the mid point between any 2 points between the 2 parallel sides of the trapezoid.

Thus get any points each on the 2 lines. (for ease we take the y-intercept).
THus the 2 points are (0,5) and (0,9)

The mid point between the 2 points will be,
( (0+0)/2 , (5+9)/2) = (0,7)

Substitute this point and the gradient of -1 into the equation of the line.
y=mx+c
7 = (-1)(0) +c
c= 7

Eqn. of midsegment, y= -x+7

Answer 2

thanks that helped alot!

Answer 3

it says it is wrong?

Answer 4

the choices are y=-x-2
y=-1/2x+7
y=x=2
y=-x=7

Answer 5

hmm im quite sure i didnt do it wrongly.
Your option
y=-x=7 looks pretty close to my answer. Is there some error in the option.

Answer 6

ahhh i guess ill have to figure it out

Answer 7

MY BAD. JUST NOTICE MY MISTAKE.
Corrected version:

Thus get any points each on the 2 lines. (for ease we take the y-intercept).
THus the 2 points are (0,5) and (0,-9)

The mid point between the 2 points will be,
( (0+0)/2 , (5-9)/2) = (0,-2)

Substitute this point and the gradient of -1 into the equation of the line.
y=mx+c
-2 = (-1)(0) +c
c= -2

Eqn. of midsegment, y= -x-2

Answer 8

ohh thank you!!!!!