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What are the coordinates of point B in the xy-plane above ?

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What are the coordinates of point B in the xy-plane above ? [#permalink]

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New post 20 Nov 2015, 00:59
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A
B
C
D
E

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  45% (medium)

Question Stats:

70% (01:28) correct 30% (01:15) wrong based on 129 sessions

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What are the coordinates of point B in the xy-plane above ?

(A) (6, 12)
(B) (6, 28)
(C) (8, 20)
(D) (12, 20)
(E) (14, 28)

Attachment:
Untitled-1.jpg
Untitled-1.jpg [ 8.39 KiB | Viewed 1575 times ]

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Re: What are the coordinates of point B in the xy-plane above ? [#permalink]

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New post 20 Nov 2015, 02:30
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Triangles ABD and CDB are congruent (RHS congruence)
∠ BDA= ∠ BDC
AB = BC
BD=BD (Common side)

Therefore , AD=DC
D is the midpoint of AC
D is (6,0)

Since AC = BD
We know AC = 28
Therefore B is (6,28)

Answer B
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Re: What are the coordinates of point B in the xy-plane above ? [#permalink]

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New post 12 Nov 2017, 06:48
Skywalker:

How did u get AC as 28?

Did u find the slope between AC

Please clarify!

Thanks in Advance!
S
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Re: What are the coordinates of point B in the xy-plane above ? [#permalink]

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New post 12 Nov 2017, 06:57
1
shinrai15 wrote:
Skywalker:

How did u get AC as 28?

Did u find the slope between AC

Please clarify!

Thanks in Advance!
S


Hi shinrai,
I found AC using the coordinates of A (-8,0) and C (20,0).
You can use the distance formula but since Y coordinates are 0 , you can simply subtract.

Hope this helps!! :-)
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What are the coordinates of point B in the xy-plane above ? [#permalink]

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New post 12 Nov 2017, 09:42
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Bunuel wrote:
Image
What are the coordinates of point B in the xy-plane above ?

(A) (6, 12)
(B) (6, 28)
(C) (8, 20)
(D) (12, 20)
(E) (14, 28)

Attachment:
Untitled-1.jpg

Given (AB = BC): This triangle is isosceles.

The altitude, BD, of an isosceles triangle is a perpendicular bisector of the opposite side, which creates two congruent right triangles with equal bases, AD and DC.

Because the altitude is both perpendicular and a bisector, the x-coordinate of D also will be the x-coordinate of B.

To find the x-coordinate of D, and hence of vertex B, use midpoint formula:

\(\frac{x_1 + x_2}{2}=\frac{-8 + 20}{2}=\frac{12}{2}=\) 6

To find y-coordinate of vertex B, use given information that AC = BD. To find distance between two points that lie on the same line (y = 0), subtract x-coordinates of A and C*:

20 - (-8) = (20 + 8) = 28 = AC
AC = BD = 28. B's y-coordinate = 28

B = (6,28)

Answer B

* You also can just "count": From -8 to 0 = distance of 8. From 0 to 20 = distance of 20. (8 + 20) = 28
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What are the coordinates of point B in the xy-plane above ?   [#permalink] 12 Nov 2017, 09:42
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