Triangle DEF has vertices of D (-7, -1), E (-7, -8), and F (1, -8). Which of these statements is true about sides DE and EF?
A.
Side EF has a length of 6 units and is longer than side DE.
B.
Side DE has a length of 7 units and is longer than side EF.
C.
Side EF has a length of 8 units and is longer than side DE.
D.
Side DE has a length of 9 units and is longer than side EF.
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To find the lengths of sides DE and EF, we can use the distance formula. The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For side DE:
D (-7, -1)
E (-7, -8)
Using the distance formula:
DE = sqrt((-7 - (-7))^2 + (-8 - (-1))^2)
= sqrt(0^2 + (-7)^2)
= sqrt(0 + 49)
= sqrt(49)
= 7
For side EF:
E (-7, -8)
F (1, -8)
Using the distance formula:
EF = sqrt((1 - (-7))^2 + (-8 - (-8))^2)
= sqrt((1 + 7)^2 + (0)^2)
= sqrt(8^2 + 0)
= sqrt(64)
= 8
Comparing the lengths of sides DE and EF, we can see that side DE (with a length of 7 units) is shorter than side EF (with a length of 8 units).
Thus, the correct statement is:
C. Side EF has a length of 8 units and is longer than side DE.
To determine the lengths of sides DE and EF, we can use the distance formula. The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of two points, and d is the distance between them.
For side DE, the coordinates are D (-7, -1) and E (-7, -8). Plugging these values into the distance formula, we get:
DE = sqrt((-7 - (-7))^2 + (-8 - (-1))^2) = sqrt(0^2 + (-7)^2) = sqrt(0 + 49) = sqrt(49) = 7
Therefore, side DE has a length of 7 units.
For side EF, the coordinates are E (-7, -8) and F (1, -8). Plugging these values into the distance formula, we get:
EF = sqrt((1 - (-7))^2 + (-8 - (-8))^2) = sqrt(8^2 + 0^2) = sqrt(64 + 0) = sqrt(64) = 8
Therefore, side EF has a length of 8 units.
Comparing the lengths, we can see that side DE has a length of 7 units, while side EF has a length of 8 units. Thus, statement C, "Side EF has a length of 8 units and is longer than side DE," is the correct answer.