Question

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

Answer 1

ABC is a triangle, with area `29`

Explanation:

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`