Question

The corners of a triangle are (2,1), (3,4), and (0,5). What is the area?

A) 4 square units
B) 5 square units
C) 6 square units
D) 7 square units

Answer 1

The area of a triangle given three vertices (2,1), (3,4), and (0,5) is calculated using the determinant method, ending up as 5 square units, which is answer B.

Step-by-step explanation:

The area of a triangle whose vertices are given can be calculated using the determinant method. For vertices (2,1), (3,4), and (0,5), the area is determined by taking the absolute value of one half times the determinant of a matrix formed by the vertices coordinates, including a column of ones. The formula is: Area = (1/2) |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|.

Using the given vertices, the area calculation is as follows:

Area = (1/2) |2(4 - 5) + 3(5 - 1) + 0(1 - 4)|

= (1/2) |2(-1) + 3(4) + 0(-3)|

= (1/2) |-2 + 12 + 0|

= (1/2) |10|

= 5 square units