In the top right corner of each question, you will see an option to check answer. Click this to check your answer before submitting. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question. Triangle ABC has vertices as shown. What is the area of the triangle? (1 point) Responses 27–√ square units 2 square root of 7 square units 10.5 square units 10.5 square units 21 square units 21 square units 15−−√ square units square root of 15 square units

Question

In the top right corner of each question, you will see an option to check answer. Click this to check your answer before submitting. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question. Triangle ABC has vertices as shown. What is the area of the triangle? (1 point) Responses 27–√ square units 2 square root of 7 square units 10.5 square units 10.5 square units 21 square units 21 square units 15−−√ square units square root of 15 square units

Answer 1

To find the area of a triangle, you can use the formula:

Area = 1/2 * base * height

First, we need to find the base and height of the triangle.

The base of the triangle is the distance between points A and B. Using the distance formula, we have:

AB = √((6-(-3))^2 + (1-4)^2)
AB = √(9^2 + (-3)^2)
AB = √(81 + 9)
AB = √90

The height of the triangle is the distance from point C to the line segment AB. We can see that the height is 3 units.

Now, plug the base and height into the formula:

Area = 1/2 * √90 * 3
Area = 1/2 * 3√90
Area = 1.5√90
Area = 1.5√(9*10)
Area = 1.5 * 3√10
Area = 4.5√10

Therefore, the area of triangle ABC is 4.5√10 square units.

Correct answer: 4.5√10 square units Check answer.