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

Answer:

The perimeter of the square LAMP is 8[tex]\sqrt{10}[/tex] units

Step-by-step explanation:

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

d = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]

∵ 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 = [tex]\sqrt{(4 - -2)^{2}+(-1--3)^{2}}[/tex]

∴ LA = [tex]\sqrt{(4+2)^{2}+(-1+3)^{2}}[/tex]

∴ LA = [tex]\sqrt{(6)^{2}+(2)^{2}}[/tex]

∴ LA = [tex]\sqrt{36+4}[/tex] = [tex]\sqrt{40}[/tex]

→ Simplify the root

∴ LA = 2[tex]\sqrt{10}[/tex] units

∵ The perimeter of the square = 4 × side

∴ The perimeter of the square = 4 × 2[tex]\sqrt{10}[/tex]

∴ The perimeter of the square = 8[tex]\sqrt{10}[/tex]

∴ The perimeter of the square LAMP is 8[tex]\sqrt{10}[/tex] units

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