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In the rectangular coordinate system above, if the area of right trian
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07 Dec 2022, 03:34
07 Dec 2022, 03:34
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85% (01:18) correct
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In the rectangular coordinate system above, if the area of right triangle DEF is 15, then which of the following are the coordinates of point D ?
(−4, −1)
(−2, −1)
(−2, 4)
(1, −1)
It cannot be determined from the information given.
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Joined: 20 Feb 2017
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Re: In the rectangular coordinate system above, if the area of right trian
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08 Dec 2022, 23:03
08 Dec 2022, 23:03
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Expert Reply
Given Area = 15
observation: Right-angled triangle at F
Distance between E and F = 4 - (-1) = 5
(as parallel to the y-axis, the difference of distance of y co-ordinates is considered else the distance formula to be used)
Now using the area formula 1/2*b*h = 15
ie, 1/2*b*5 = 15
ie, b = 6
as DF is parallel to the x-axis, the difference in the x-axis is considered
4 - x1 = 6
x1 = -2
therefore coordinates (-2,-1)
Answer: B
observation: Right-angled triangle at F
Distance between E and F = 4 - (-1) = 5
(as parallel to the y-axis, the difference of distance of y co-ordinates is considered else the distance formula to be used)
Now using the area formula 1/2*b*h = 15
ie, 1/2*b*5 = 15
ie, b = 6
as DF is parallel to the x-axis, the difference in the x-axis is considered
4 - x1 = 6
x1 = -2
therefore coordinates (-2,-1)
Answer: B
Re: In the rectangular coordinate system above, if the area of right trian
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11 Dec 2022, 04:00
11 Dec 2022, 04:00
Expert Reply
OE
Subtracting the y-coordinates of the given points gives you the length of leg EF: 4 − (−1) = 5. The area formula for a triangle will give you the length of the other leg, DF: 1/2 * bh=1/2 * b* 5 , to give an area of 15. Subtracting 6 from the x-coordinate of F gives you the x-coordinate of D, and D has the same y-coordinate as F. So the coordinates of D are (−2, −1); the answer is choice (B).
Subtracting the y-coordinates of the given points gives you the length of leg EF: 4 − (−1) = 5. The area formula for a triangle will give you the length of the other leg, DF: 1/2 * bh=1/2 * b* 5 , to give an area of 15. Subtracting 6 from the x-coordinate of F gives you the x-coordinate of D, and D has the same y-coordinate as F. So the coordinates of D are (−2, −1); the answer is choice (B).
