The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle

Question

The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?

A. 102
B. 120
C. 132
D. 144
E. 156

Kudos for a correct  solution .

Bunuel · Accepted Answer

MAGOOSH OFFICIAL SOLUTION: righttrianglearea_text.PNG

Lucky2783 · Answer

B and C should have same Y co-ordinate -->  4a-5 = 2a+6  --> a= \frac{11}{2}

area of triangle =  \frac{1}{2} * (4a-5) * (2a+1)  . on substituting a= \frac{11}{2}  
we get area = 102 .

answer A

AmoyV · Answer

1/2bh=1/2(2a+1)(2a+6)

Now 4a-5=2a+6
2a=11

Therefore,
A(0,0); B(0,17); C(12,17)

1/2*17*12=102

Answer: A

Aksena · Answer

Sorry, but I did not get to your calculations - why it is so? What I missed?

blazeowlss · Answer

Im guessing you have problems understanding why 4a-5 = 2a+6

Now, the reason they got to that equation was due to the given information that angle ABC = 90
--> This implies that triangle ABC was a right angle 
--> Now A was given at the origin (0,0), while B was given to be somewhere along the Y-axis as its X-coordinates = 0 
--> Hence, as ABC was a right triangle, the point C will have the  same Y-coordinates  as B in order to form the right triangle (i.e. to fulfill angle A B C = 90)
--> B(0, 4a-5 ) and C(2a+1,  2a+6 )
--> Therefore 4a-5 = 2a+6, solve for a and you can find the area of the triangle with the basic area formula for right triangles: base x height / 2

ScottTargetTestPrep · Answer

Since we have a right triangle with angle ABC = 90, we see that vertices A and B share the same x-coordinate, and vertices B and C share the same y-coordinate.

Equating the y-coordinates of vertices B and C, we have:

4a - 5 = 2a + 6

2a = 11

a = 5.5

Substituting 5.5 for a, we see that the ordered pair for vertex B is (0, 4(5.5) - 5), or (0, 17). Thus, leg AB is the vertical distance from (0,0) to (0,17), or 17.
Similarly, we see that the ordered pair for vertex C is (12, 17) and leg BC is is the horizontal distance from (0,17) to (12, 17) = 12.

Thus, the area of the triangle is:

area = base x height x 1/2

area = 17 x 12 x 1/2 = 17 x 6 = 102

Answer: A

Fdambro294 · Answer

If the 90 degree angle is Angle <ABC

Then this means the 90 degree angle is at Vertex B

Points A and B both appear on the Y Axis

Therefore, we need side BC to be Perpendicular to the Y Axis ——-> and the Y coordinate of point C will equal the Y coordinate of point B

Setting the 2 Y coordinates equal

4a - 5 = 2a + 6

2a = 11

a = 5.5

Point B = (0 , 17)

Point C = (12 , 17)

Point A = (0 , 0)

The vertical leg on the Y Axis will extend from A to B and equal 17 units

The perpendicular/Horizontal Leg —side CB — will extend from (0 , 17) ———> (12 , 17)

Or 12 units

Area = (1/2) (12) (17) =

102

Posted from my mobile device

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The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle

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The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle

Prep Toolkit

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