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?

The answer is below

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Rotation is the rotation of an object about a fixed point. If a point A(x, y) is rotated 180° around the origin, the new point is at A'(-x, -y).

Let us assume that the vertex of triangle LMN is at L(0, 0), M(5, 0) and N(0, 4). Hence if a triangle LMN is rotated 180° around the origin, the new triangle is at L'(0, 0), M'(-5, 0) and N'(0, -4).

If a line is drawn through points L and L′ and through M and M′, we can see that the line passes through the origin. Also if the line is drawn through points N and N′ it passes through the origin.

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)