Graph a triangle (LMN) and reflect it over the line y=x to create triangle L'M'N'. Describe the transformation using words. Draw a line segment from point L to the reflecting line, and then draw a line segment from point L' to the reflecting line. What do you notice about the two line segments you drew? Do you think you would see the same characteristic if you drew the line segment connecting M with the reflecting line and then M' with the reflecting line? How do you know? (10 points)

1) The reflection of a preimage (x, y) across the line y = x gives the image (y, x)

Therefore, the the coordinates of the points L, M, and N interchange to give an image of the triangle that is apparently rotated 90° clockwise, on the opposite quadrant and equidistant from the line y = x

2) Where the line segment drawn from point L to the reflecting line is horizontal, and the line segment drawn from point L to the reflecting line is horizontal, the two line segment will be of the same length and separated vertically separated vertically by a distance equal to the sum of the absolute values of the x and y coordinates of the point L

When the line segment from point L is drawn perpendicular to the reflecting line, the line segment from point L' drawn perpendicular to the reflecting line will meet the the perpendicular line segment at the same point of intersection of the line from the point L and the reflecting line

3) Yes

4) This is so because, reflection of a preimage unto an image is a form of rigid transformation, therefore, the effect of the transformation operation will be similar when each point is individually considered.

Step-by-step explanation:

1. minimum

2. 6400

3. eight

hope this !

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²