Graph a triangle (LMN) and rotate it 180° around the origin to create triangle L′M′N′. Describe the transformation using words. Make sure you refer to the characteristics and the coordinates. Draw a line through points L and L′ and through M and M′. What do you notice about the lines you drew? Do you think you would notice the same characteristics if you drew another line through points N and N′? How do you know?

d≈7.07in

step-by-step explanation:

n=1.75+1.75

step-by-step explanation:

3.5/2=1.75

once you solve it out the value of x is 13

  b:   ∠x = 28.6°, ∠y = 31.2°, ∠z = 120.2°

step-by-step explanation:

this is one of those questions where "test taking skill" is all you need. the only answer that has angles that sum to 180° is the one shown above. the remaining choices do not describe the angles of a triangle.

if you want to do more work than simply adding the offered numbers, you can also check them against the law of sines. it should be true that

  x/sin(x) = y/sin(y) = z/sin(z)

and all of these ratios must be greater than 15, the longest side length.

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if you want to solve the triangle from scratch, i'd suggest solving for the largest angle using the law of cosines.

  z² = x² +y² -2xy·cos(z)

  z = arccos((x² +y² -z²)/(2xy)) = arccos(-75.11/149.4) = 120.182°

now you can find y from the law of sines

  y = arcsin(y/z·sin(z)) = 31.242°