Question

Square LAMP has vertices L(-2, -3), A(4, -1), M(2,5), and P(-4, 3). What is the

Answer 1

Answer:

The perimeter of the square LAMP is 8$\sqrt{10}$ units

Step-by-step explanation:

The rule of the distance between two points (x1, y1) and (x2, y2) is

d = $\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$

∵ LAMP is a square

∵ The sides of the square are equal in lengths

∴ LA = AM = MP = PL

Let us find the length of one side of it

∵ L = (-2, -3) and A = (4, -1)

∴ x1 = -2 and y1 = -3

∴ x2 = 4 and y2 = -1

→ Substitute them in the rule of the distance above to find LA

∵ LA = $\sqrt{(4 - -2)^{2}+(-1--3)^{2}}$

∴ LA = $\sqrt{(4+2)^{2}+(-1+3)^{2}}$

∴ LA = $\sqrt{(6)^{2}+(2)^{2}}$

∴ LA = $\sqrt{36+4}$ = $\sqrt{40}$

→ Simplify the root

∴ LA = 2$\sqrt{10}$ units

∵ The perimeter of the square = 4 × side

∴ The perimeter of the square = 4 × 2$\sqrt{10}$

∴ The perimeter of the square = 8$\sqrt{10}$

∴ The perimeter of the square LAMP is 8$\sqrt{10}$ units