TS Exam 2, QR #14, Confused!

[tawaqul]

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In a 2-d coordinate system, point A= (3,-6), point B = (1,1), and point C= (7,6). Find the area of triangle ABC.

I tried drawing it out and using the distance formula to figure out the lengths of the sides, but you need the height (area of a tri= 1/2BH). I am not getting the correct answer which is 26.

Someone please explain!

Thanks in advance!

 

[Streetwolf]

In a 2-d coordinate system, point A= (3,-6), point B = (1,1), and point C= (7,6). Find the area of triangle ABC.

I tried drawing it out and using the distance formula to figure out the lengths of the sides, but you need the height (area of a tri= 1/2BH). I am not getting the correct answer which is 26.

Someone please explain!

Thanks in advance!

Relocate one point to (0,0), relocate the other 2 points, then find the determinant of those 2 points. The absolute value of the determinant is the area of the parallelogram made by those points so when you divide that by 2 you'll get the area of the triangle.

Use (1,1) and relocate to (0,0) by subtracting 1 on the x and 1 on the y. Then for the other two points you get A = (2, -7) and C = (6, 5). The determinant is (6)(-7) - (2)(5) = -52 (or you could do (2)(5) - (-7)(6) = 52. Either way the absolute value is 52). Divide that by 2 and you get 26, your answer.

Still confused? Google determinant for an explanation.

 

[Electrons]

If point B is (1,2), can you sub 1 on the X and sub 2 on the Y then apply same rule in sub 1 to the other 2 Xs and sub 2 to the other 2 Ys and do the determinant?

Relocate one point to (0,0), relocate the other 2 points, then find the determinant of those 2 points. The absolute value of the determinant is the area of the parallelogram made by those points so when you divide that by 2 you'll get the area of the triangle.

Use (1,1) and relocate to (0,0) by subtracting 1 on the x and 1 on the y. Then for the other two points you get A = (2, -7) and C = (6, 5). The determinant is (6)(-7) - (2)(5) = -52 (or you could do (2)(5) - (-7)(6) = 52. Either way the absolute value is 52). Divide that by 2 and you get 26, your answer.

Still confused? Google determinant for an explanation.

 

[Streetwolf]

If point B is (1,2), can you sub 1 on the X and sub 2 on the Y then apply same rule in sub 1 to the other 2 Xs and sub 2 to the other 2 Ys and do the determinant?

Yes. This just moves the triangle left 1 and down 2. The points do not move relative to each other. If instead I used (7, 6) then I'd subtract 7 from the x and 6 from the y. I'd get the points (-6, -5) and (-4, -12). The determinant would be (-6)(-12) - (-4)(-5) = 72 - 20 = 52. Same thing.

 

[Andre3k]

Are the QR questions on Topscore realistic? Cause some of them are pretty time consuming.