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AD is an altitude of an isosceles triangle ABC such that it bisects th
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28 Aug 2023, 03:24
28 Aug 2023, 03:24
Expert Reply
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Question Stats:
60% (02:35) correct
40% (02:24) wrong based on 5 sessions
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AD is an altitude of an isosceles triangle ABC such that it bisects the base BC. Co-ordinates of A and D are (3, 1) and (3, –2) respectively. If the area of the triangle is 12 sq units, which of the following could be the coordinate of point B?
Indicate all that apply
A. (7, 1)
B. (–4, 3)
C. ( –1, 1)
D. (–1, –2)
E. (7, –2)
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Indicate all that apply
A. (7, 1)
B. (–4, 3)
C. ( –1, 1)
D. (–1, –2)
E. (7, –2)
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
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Re: AD is an altitude of an isosceles triangle ABC such that it bisects th
[#permalink]
18 Sep 2023, 03:48
18 Sep 2023, 03:48
Expert Reply
OE
In triangle 𝐴𝐵𝐶, 𝐴𝐷 = 3 units. (Using distance formula, we can find length of line
segment AD)
Area of triangle 𝐴𝐵𝐶 = 12 square units
As we know that area of a triangle =1/2*b*3=12
b=8
𝐵𝐶 = 8 units.
As 𝐵𝐶 is bisected at 𝐷, 𝐷𝐵 = 4
Across segment 𝐵𝐶, only 𝑥 -coordinate of point 𝐷 would change, 𝑦 -coordinate will
remain -2.
So, on positive side of Point 𝐷, 𝑥 - coordinate of point 𝐵 would be 4 + 3 = 7.
On negative side of Point 𝐷, 𝑥 -coordinate of point 𝐵 would be 3 – 4 = -1
Therefore, possible coordinates of 𝐵 are: (7, -2) or (-1, -2).
Ans. (D and E)
In triangle 𝐴𝐵𝐶, 𝐴𝐷 = 3 units. (Using distance formula, we can find length of line
segment AD)
Area of triangle 𝐴𝐵𝐶 = 12 square units
As we know that area of a triangle =1/2*b*3=12
b=8
𝐵𝐶 = 8 units.
As 𝐵𝐶 is bisected at 𝐷, 𝐷𝐵 = 4
Across segment 𝐵𝐶, only 𝑥 -coordinate of point 𝐷 would change, 𝑦 -coordinate will
remain -2.
So, on positive side of Point 𝐷, 𝑥 - coordinate of point 𝐵 would be 4 + 3 = 7.
On negative side of Point 𝐷, 𝑥 -coordinate of point 𝐵 would be 3 – 4 = -1
Therefore, possible coordinates of 𝐵 are: (7, -2) or (-1, -2).
Ans. (D and E)
gmatclubot
Re: AD is an altitude of an isosceles triangle ABC such that it bisects th [#permalink]
18 Sep 2023, 03:48
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