Question

how do you find the perimeter of a rectangle with these vertices

A(-1,1)
B(3,4)
C(6,0)
D(2,-3)

Answer 1

Question#29499

how do you find the perimeter of a rectangle with these vertices

A(-1,1)

B(3,4)

C(6,0)

D(2,-3)

**Solution.** The formula for a distance between two points $M(x_{1},y_{1}), N(x_{2},y_{2})$:

$$d(M, N) = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}.$$

Thus, $AB = \sqrt{(-1 - 3)^2 + (1 - 4)^2} = \sqrt{16 + 9} = 5$

$$BC = \sqrt{(3 - 6)^{2} + (4 - 0)^{2}} = \sqrt{9 + 16} = 5$$ $$CD = \sqrt{(6 - 2)^{2} + (0 - (-3))^{2}} = 5$$ $$AD = \sqrt{(-1 - 2)^{2} + (1 - (-3))^{2}} = 5.$$

Finally, the perimeter $P = AB + BC + CD + AD = 5 + 5 + 5 + 5 = 20$.

**Answer.** $P = 20$.