If (x1, y1), (x2, y2) and (x3, y3) are three vertices of a triangle AB

Question

If  (x_1, y_1) ,  (x_2, y_2)  and  (x_3, y_3)  are three vertices of a triangle ABC, what is the area of the triangle ABC?

(1)  x_1 = -2 ,  x_2 = -3 ,  x_3 = 4 ,  y_1 = 3 ,  y_2=-1 ,  y_3=-5

(2)  x_1*y_2=2 ,  x_2*y_3=15 ,  x_3*y_1=12 ,  x_3*y_2=-4 ,  x_1*y_3=10  and  x_2*y_1=-9

ocelot22 · Answer

(1) we have the coordinates for all three vertices. this is enough info to calculate the area. we can use the distance formula to calculate side lengths of our triangle, and very easily construct a rectangle around our triangle. Find the area of the rectangle, and then subtract the area of the three associated right triangles that are formed. Sufficient

(2) We have 6 equations here, for 6 variables, but these are all proportional. we have enough info to reduce this system down in terms of one of the variables. For example, we can reduce this system down in terms of y3, for example x1 = 10/y3, x2 = 15/y3, x3 = -20/y3 y1 = -3y3/5, y2 = y3/5, and y3=y3

so our coordinates would be (10/y3, -3y3/5), (15/y3, y3/5), and (-20/y3,y3). All of these depend on variable y3, so depending on our choice of y3, we will have different coordinates and a different area. You could reduce the system down in terms of any of the other 5 variables. the main point here, is that we will never be able to know the coordinates, because our coordinates will be in terms of one of our variables, so we will get different areas depending on our choice of that variable. NS

OA is A

CEdward · Answer

Can someone explain whether the answer is in fact A or D?

AkashM · Answer

Its D.

For statement 2, you can use the determinant method to find the area of the triangle.

Abdeviliiers · Answer

Indeed by the determinant method we can solve using statement 2 as well (a google search will give the formula)

I however doubt if the GMAT ever tests this aspect!!

Resily · Answer

Bunuel , need your help to understand why the answer is D. I see there are 6 variables and 6 equations, but unless these equations are solvable we can't conclude D. Also, there is always an efficient way to look at GMAT problems - guide us please!

If (x1, y1), (x2, y2) and (x3, y3) are three vertices of a triangle AB

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If (x1, y1), (x2, y2) and (x3, y3) are three vertices of a triangle AB

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards