Question

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

A) 12.5 square units
B) 17.5 square units
C) 19.5 square units
D) 22.5 square units

Answer 1

19.5

Explanation:

Use the distance formula: d =

(x2 - x1)2 + (y2 - y1)2

A =

1

2

bh =

1

2

(

13

)(3

13

) = 19.5

Answer 2

C) 19.5 square units

Explanation:

The area from coordinates can be computed as ...

A = (1/2)|x1(y2 -y3) +x2(y3 -y1) +x3(y1 -y2)|

= (1/2)|7(10 -4) +0(4 -1) +9(1-10)| = (1/2)|7·6 +9·(-9)|

= (1/2)|-39| = 39/2 = 19.5

The area of the triangle is 19.5 square units.