Question

Find the area of the triangle defined by the coordinates (7,1). (0, 10), and (9,4). (To the nearest tenth)

Answer 1

Answer:

19.5

Step-by-step explanation:

The area of a triangle given 3 coordinates can be solved using the formula:

$Area=|\frac{A_x(B_y-C_y)+B_x(C_y-A_y)+C_x(A_y-B_y)}{2}|$

Where

A_x is x coordinate of first point (here 7)

A_y is y coordinate of first point (here 1)

B_x is x coordinate of 2nd point (here 0)

B_y is y coordinate of 2nd point (here 10)

C_x is x coordinate of 3rd point (here 9)

C_y is y coordinate of 3rd point (here 4)

Plugging these into the formula, we get out answer:

$Area=|\frac{A_x(B_y-C_y)+B_x(C_y-A_y)+C_x(A_y-B_y)}{2}|\\Area=|\frac{7(10-4)+0(4-1)+9(1-10)}{2}|\\Area = |\frac{7(6)+0+9(-9)}{2}|\\Area=|-19.5|\\Area = 19.5$

Hence, the area is 19.5