Question

find the perimeter of triangle ABC if A(1,1), B(4,-3), and C(-3,-2)

Answer 1

10 +5√2

To find the perimeter of a triangle, let's use a formula derived from the Pythagorean Theorem:

$d\text{ =}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

2) So let's calculate the length of the segment AB. A(1,1) and B (4,-3)

$d=\sqrt[]{(4-1)^2+(-3-1)^2}=5$

The segment BC , B(4,-3) and C(-3,-2)​:

$d=\sqrt[]{(-3-4)^2+(-2+3)^2}=5\sqrt[]{2}$

And finally, the segment AC: A(1,1) and C(-3,-2)​

$d=\sqrt[]{(-3-1)^2+(-2-1)^2}=5$

3) The Perimeter is the sum of the lengths: 5 + 5 +5√2 = 10 +5√2