What is the area of a triangle with vertices at (−4, 1) , (−7, 5) , and (0, 1) ? enter your answer in the box.

The area of a shape is the amount of space it occupies.

The area of the triangle is 8 unit square.

The vertices are given as:

The area of the triangle is:

So, we have:

Remove absolute brackets

Hence, the area of the triangle is 8 unit square.

Read more about areas at:

link

we know that

A method for calculating the area of a triangle when you know the lengths of all three sides is the Heron's Formula.

The Heron's Formula states that

where

a,b.c are the length sides of the triangle

p is half the perimeter of the triangle

Let

Step 1

Find the distance AB

we know that

the formula to calculate the distance between two points is equal to

we have

substitute the values in the formula

Step 2

Find the distance BC

we know that

the formula to calculate the distance between two points is equal to

we have

substitute the values in the formula

Step 3

Find the distance AC

we know that

the formula to calculate the distance between two points is equal to

we have

substitute the values in the formula

Step 4

Find half the perimeter

substitute the values

Step 5

Find the area

Applying the Heron's Formula

therefore

the answer is

the area of the triangle is  

step-by-step explanation:

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .