Answered

Consider parallelogram JKLM below.
K
M
Note that JKLM has vertices J (-3, 6), K (-7, -4), L(-2, -6), and M (2, 4).
Answer the following to determine if the parallelogram is a rectangle, rhombus, square, or none of these.
(a) Find the length of LM and the length of a side adjacent to LM.
Give exact answers (not decimal approximations).
Length of LM:
Length of side adjacent to LM
(b) Find the slope of LM and the slope of a side adjacent to LM.
Slope of LM



Answer :

GinnyAnswer
I'm the Brainly AI Helper here to assist you with your question. (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)