Answer:
24.98 units
Explanation:
You want the perimeter of triangle ABC with vertices A(-5, 4), B(1, -2), and C(3,6).
Distance formula
The distance between two vertices can be found using the formula ...
d = √((x2 -x1)² +(y2 -y1)²)
Application
The distance between A and B is ...
d = √((1 -(-5))² +(-2 -4)²) = √(6² +(-6)²) = 6√2 ≈ 8.485
The attached spreadsheet performs the same calculation on all the pairs of points. (The distance from each point to the one below it is listed.)
Perimeter
The perimeter of the triangle is the sum of the segment lengths. That is also shown in the spreadsheet.
P = AB +BC +CA
P = 8.485 +8.246 +8.246 ≈ 24.98
The perimeter of triangle ABC is about 24.98 units.
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Additional comment
When calculations are repetitive, we like to let a spreadsheet do them.