A triangle is formed by the points A(-1,1) B(4,3) and C (0,13)?

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Answer 1 · 2015-07-20T09:49:09

ABC is a triangle, with area #29#

Slope #m# between two points #(x_1, y_1)# and #(x_2, y_2)# is given by the formula:

#m = (Delta y)/(Delta x) = (y_2 - y_1) / (x_2 - x_1)#

The slope of a line through #A# and #B# is:

#m_(AB) = (3 - 1) / (4 - (-1)) = 2/5#

The slope of a line through #A# and #C# is:

#m_(AC) = (13-1) / (0 - (-1)) = 12#

So these three points are not colinear and do form the vertices of a triangle.

Let #ul v_(AB) = B-A = (5, 2)# and #ul v_(AC) = C-A = (1,12)#

Then the area of the triangle is:

#1/2abs(ul v_(AB) xx ul v_(AC)) = 1/2abs(5*12-2*1) = 1/2abs(58) = 29#