Answer :
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(a)
Length of LM:
To find the length of LM, you can use the distance formula:
Length of LM = √((x2 - x1)^2 + (y2 - y1)^2)
Given points L(-2, -6) and M(2, 4):
Length of LM = √((2 - (-2))^2 + (4 - (-6))^2)
Length of LM = √(4^2 + 10^2)
Length of LM = √(16 + 100)
Length of LM = √116 (exact answer)
Length of side adjacent to LM:
To find the length of a side adjacent to LM, you can calculate the distance between two adjacent points. Let's take LM and KL:
KL: K(-7, -4)
Length of KL = √((-7 - (-2))^2 + (-4 - (-6))^2)
Length of KL = √((-7 + 2)^2 + (-4 + 6)^2)
Length of KL = √((-5)^2 + (2)^2)
Length of KL = √(25 + 4)
Length of KL = √29 (exact answer)
(b)
Slope of LM:
To find the slope of LM, you can use the formula:
Slope = (y2 - y1) / (x2 - x1)
Given points L(-2, -6) and M(2, 4):
Slope of LM = (4 - (-6)) / (2 - (-2))
Slope of LM = 10 / 4
Slope of LM = 5/2 or 2.5 (exact answer)
Slope of a side adjacent to LM:
To find the slope of a side adjacent to LM, you can calculate the slope between two adjacent points. Let's take LM and JK:
JK: J(-3, 6)
Slope of JK = (6 - 6) / (-3 - 2)
Slope of JK = 0 / -5
Slope of JK = 0 (exact answer)