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

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Joined: 02 Sep 2009
Posts: 59722
What are the coordinates of point B in the xy-plane above ?  [#permalink]

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20 Nov 2015, 00:59
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:00) correct 33% (01:57) wrong based on 218 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)

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Untitled-1.jpg [ 8.39 KiB | Viewed 3124 times ]

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

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20 Nov 2015, 02:30
4
Triangles ABD and CDB are congruent (RHS congruence)
∠ BDA= ∠ BDC
AB = BC
BD=BD (Common side)

D is the midpoint of AC
D is (6,0)

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

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

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12 Nov 2017, 06:48
Skywalker:

How did u get AC as 28?

Did u find the slope between AC

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

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12 Nov 2017, 06:57
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shinrai15 wrote:
Skywalker:

How did u get AC as 28?

Did u find the slope between AC

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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12 Nov 2017, 09:42
4
Bunuel wrote:

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)

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

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18 Jul 2019, 17:39
Simply using the information given to derive some facts can help a lot.

I'm a visual learner so I don't like reading a bunch of text explaining why things are the way they are.

So just quickly in relation to my diagram

We are told AB = BC
Therefore <ADB must be 90 degrees also

We are told AC = BD = 28 so write this in
This is common to both triangles, so <BAD = <BCA

Since two angles and two sides are equal the third angle (marked in green) and corresponding side must also be equal.

This allows us to conclude that D must be the midpoint of AC as the | must each equal each other

From here we can ascertain the midpoint as (20+(-8))/2 = 12/2 = 6

The y coordinate must be 28 since the height, BD, is 28

Thus, (6,28)
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Re: What are the coordinates of point B in the xy-plane above ?  [#permalink]

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29 Nov 2019, 01:37
Use distance formulae AB=BC given
Let point B be (x,y)
so, sqrt[(x-(-8))^2+(y-0)^2]=sqrt[(20-x)^2+(0-y)^2]
or, 16x+64=400-40x
or, x=6

This gives coordinate of D i.e. (6,0)
Given, AC=BD
use again distance formulae.
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Re: What are the coordinates of point B in the xy-plane above ?   [#permalink] 29 Nov 2019, 01:37
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