Answers:
- Part A) There is one pair of parallel sides
- Part B) (-3, -5/2) and (-1/2, 5/2)
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Explanation:
Part A
By definition, a trapezoid has exactly one pair of parallel sides. The other opposite sides aren't parallel. In this case, we'd need to prove that PQ is parallel to RS by seeing if the slopes are the same or not. Parallel lines have equal slopes.
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Part B
The midsegment has both endpoints as the midpoints of the non-parallel sides.
The midpoint of segment PS is found by adding the corresponding coordinates and dividing by 2.
x coord = (x1+x2)/2 = (-4+(-2))/2 = -6/2 = -3
y coord = (y1+y2)/2 = (-1+(-4))/2 = -5/2
The midpoint of segment PS is (-3, -5/2)
Repeat those steps to find the midpoint of QR
x coord = (x1+x2)/2 = (-2+1)/2 = -1/2
y coord = (x1+x2)/2 = (3+2)/2 = 5/2
The midpoint of QR is (-1/2, 5/2)
Join these midpoints up to form the midsegment. The midsegment is parallel to PQ and RS.
Answer:
Shira: x = 8
Samuel: m = 0
Step-by-step explanation:
Shira's mistake was that she subtracted 2 from both sides instead of adding to on both sides.
Correct Solving:
2x - 2 = 14
Add 2 to both sides;
2x = 16
Divide both sides by 2;
x = 8
Samuel's mistake was that when he distributed -2 to 8m and 8 he put the wrong sign for -2 * 8.
Correct Solving:
-2(8m + 8) = -16
Distribute;
-16m - 16 = -16
Add 16 to both sides;
-16m = 0
Divide both sides by -16;
m = 0
Answer:
Step-by-step explanation:
6-3x=12-6x
Only one solution of x=2
