1. Estimate the area of the irregular shape. Explain your method and show your work.
2. The coordinates of the vertices of △LMN are L (-2, 4), M (3, -1), and N (0, -4). Determine whether △LMN is a right triangle and support your decision. Show all work.
3. The coordinates of the vertices of quadrilateral PQRS are P (-6, 2), Q (-1, 4), R (2, 2), and S (-3, 0). Alexandra states that quadrilateral PQRS is a parallelogram. Prove or disprove Alexandra’s statement. Show all work.

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mathmate mathmate · Answer 1 · 2021-06-16T12:26:11+02:00

Answer:

Step-by-step explanation:

1. Do not see a figure, and unsafe to download and execute .docx.

2. Vectors LM<5,-5>, NM<3,3>, NL<2,-8>

Since LM.NM = 15-15 = 0, LM and NM are orthogonal, hence the given points form a right triangle.

3. A parallelogram has opposite sides parallel.

Slope PQ = (4-2) / (-1 - -6) = 2/5

Slope RS = (2-0) / (2- -3) = 2/5

Therefore PQ || RS

Slope PS = (2-0)/(-6- -3) = -2/3

Slope QR = (4-2)/(-1 -2) = -2/3

Therefore PS | QR

Since opposite sides are parallel, PQRS is a parallelogram

cwrw238 cwrw238 · Answer 2 · 2021-06-16T12:34:40+02:00

Answer:

Step-by-step explanation:

1. There are 31 complete are almost complete squares.

Top line is about 3.5 squares

Right side is about 1.8

Bottom about 3.5 and left side about 1.2.

Total approximately 41 square units.

2. If it is a right triangle then 2 sides will be perpendicular.

Slope of LM = (-1-4)/(3 +2 = -1

Slope of MN = (-4+1)/ -3 = -3/-3 = 1.

So as the product of the slope = -1 * 1 = -1 the angles between LM and MN is a right angle and LMN is a right triangle.