Triangle DEF has vertices of ,D(-7,-1),E(-7,-8), and F1,-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.
C. Side EF has a length of 8 units and is longer than side DE.
To determine which statement is true about sides DE and EF, we need to calculate the lengths of these sides. The length of a line segment can be found using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the length of side DE first:
DE = sqrt((-7 - (-7))^2 + (-8 - (-1))^2)
= sqrt(0^2 + (-7)^2)
= sqrt(0 + 49)
= sqrt(49)
= 7 units
Now, let's calculate the length of side EF:
EF = sqrt((-7 - (-7))^2 + (-1 - (-8))^2)
= sqrt(0^2 + 7^2)
= sqrt(0 + 49)
= sqrt(49)
= 7 units
From the calculations, we can see that both sides DE and EF have a length of 7 units. Therefore, none of the given statements is true.
To find the lengths of the sides DE and EF, we can use the distance formula:
Distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given the coordinates of the vertices:
D(-7,-1), E(-7,-8), and F(-1,-8)
Let's find the length of side DE:
DE = sqrt((-7 - -7)^2 + (-8 - -1)^2)
= sqrt(0^2 + (-8 + 1)^2)
= sqrt(0 + (-7)^2)
= sqrt(0 + 49)
= sqrt(49)
= 7 units
Now, let's find the length of side EF:
EF = sqrt((-1 - -7)^2 + (-8 - -8)^2)
= sqrt((-1 + 7)^2 +