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In the coordinate axis above, line segment AC is three times

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by BTGmoderatorDC » Fri Jan 03, 2020 3:56 pm
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In the coordinate axis above, line segment AC is three times as long as line segment AB. In addition, segment AC is perpendicular to segment BD. What is the area of triangle DOB?

A. 4
B. \(4\sqrt{2}\)
C. 6
D. 8
E. It cannot be determined from the information given.




OA D

Source: Princeton Review
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by swerve » Sat Jan 04, 2020 2:27 pm
BTGmoderatorDC wrote:Image

In the coordinate axis above, line segment AC is three times as long as line segment AB. In addition, segment AC is perpendicular to segment BD. What is the area of triangle DOB?

A. 4
B. \(4\sqrt{2}\)
C. 6
D. 8
E. It cannot be determined from the information given.




OA D

Source: Princeton Review
We can solve this question as follows,

1. Draw the figure w/labels
2. Now the distance from A to B is X, distance from B to C is 2X
3. Since B will have x coordinate 0 then we only need to 'y' coordinate. Now since all the height for segment AC is 6 then AB will only have height 2, then 6-2 = 4, so B (0,4)
4. Now, right triangle BOD is an isosceles right triangle with angles 45-45-90. Angle 45 corresponds to 4.

So the area is 4*4/2 = 8.

The correct answer is __D__
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