Answer:
The area of △ABC is equal to the area of △DEF
Step-by-step explanation:
On a coordinate plane, triangles A B C and D E F are shown. Triangle A B C has points (4, 2), (7, 2), (4, 6). Triangle D E F has points (negative 2, negative 1), (4, negative 3), and (4, negative 1).
How do the areas of triangle ABC and DEF compare? The area of △ABC is 1 square unit less than the area of △DEF. The area of △ABC is equal to the area of △DEF. The area of △ABC is 1 square unit greater than the area of △DEF. The area of △ABC is 2 square units greater than the area of △DEF.
Answer: The length of the sides of the triangle ABC are given below:
[tex]AB=\sqrt{(7-4)^2+(2-2)^2} =3\ unit\\\\BC=\sqrt{(4-7)^2+(6-2)^2} =5\ unit\\\\AC=\sqrt{(4-4)^2+(6-2)^2} =4\ unit[/tex]
The area of triangle ABC is given as:
Area = 1/2 × base × height = 1/2 × 3 × 4 = 6 unit²
The length of the sides of the triangle DEF are given below:
[tex]DE=\sqrt{(4-(-2))^2+(-3-(-1))^2} =\sqrt{40} \ unit\\\\EF=\sqrt{(4-2)^2+(-1-(-3))^2} =2 \ unit\\\\DF=\sqrt{(4-(-2))^2+(-1-(-1))^2} =6 \ unit[/tex]
The area of triangle DEF is given as:
Area = 1/2 × base × height = 1/2 × 2 × 6 = 6 unit²
The area of triangle ABC is equal to 6 unit² and the area of triangle DEF is equal to 6 unit² , therefore The area of △ABC is equal to the area of △DEF
