Mathematics, 04.12.2019 19:31, andersonrocksc

Which statements are true about reflections? check all that apply.

a. an image created by a reflection will always be congruent to its pre-image

b. an image and its pre-image are always the same distance from the line of reflection

c. if a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image.

d. the line of reflection is perpendicular to the line segments connecting corresponding vertices.

e. the line segments connecting corresponding vertices all congruent to each other

f. the line segments connecting corresponding vertices are all parallel to each other

Answers: 3

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A reflection transformation is a transformation in which the points on the preimage are flipped over or reflected across the reflecting line

The true statements about reflection are; statements a, b, c, d, and e

The reason the above selected options are correct are as follows;

a. An image created by a reflection will always be congruent to its preimage

The above statement is true because a reflection is a rigid transformation and the distances between each pair of points on the preimage are equal to the distances between the corresponding pair of points on the image

b. An image and its pre-image are always the same distance from the line of reflection

The above statement is true because the coordinate of the location of the image of a point (x, y) following a reflection across the x-axis is the point (x, - y), such that the vertical distances of the preimage and the image from the reflecting line which is the x-axis are both y, and -y, which is the same magnitude of distance but different sign showing difference in direction of measurement

c. If a point on the preimage lies on the line of reflection, the image of that point is the same as the pre-image

The above statement is true because, using the example of the reflection across the x-axis, if the pre-image point is located on the x-axis, the coordinate of the point is (x, 0) and using the rule of reflection across the x-axis, the coordinate of the image is (x, -0) = (x, 0), which is the same point as the preimage

d. The line of reflection is perpendicular to the line segments connecting corresponding vertices

The above statement is true, because using the example of the reflection of a line across the x-axis, the location of the preimage is (x, y), and the location of the image is (x, -y), therefore, the reflecting line bisects, perpendicularly, the line joining the point on the image and the corresponding point on the image, and therefore, the reflecting line is perpendicular to the line joining the corresponding vertices

e. The line segments connecting corresponding vertices are not all congruent to each other because the length of each line segment connecting corresponding vertices depends on the distance between the vertices and the reflecting line, which are not all always the same

f. The line segment connecting corresponding vertices are all parallel to the each other

The above statement is true, because, the line segment connecting corresponding vertices are all perpendicular to the reflecting line, and they are therefore, parallel to each other

The true statements are a, b, c, d, and f

Learn more about reflection transformation here:

link

answered: jurnee77

a. An image created by a reflection will always be congruent to its pre-image

This statement is true because a reflection is a rigid transformation, that is, it doesn't change the shape and size of the original figure, it just moves it. That's why the reflectio is congruent to its pre-image.

b. An image and its pre-image are always the same distance from the line of reflection

This statement is also true, because the line of reflection is an axis that it's a reference for each figure. Also, when we reflect a figure, we are changing some coordinates to their opposite, for example, x=-2 changes to x'=2, which means the distance from the line of reflection is the same, two units.

c. If a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image.

When we reflect a figure, and its reflected image has a points on the line of reflection, that means the pre-image also has its correspoinding point on the line of reflection, because actually that point won't change its coordinates is ON the line of reflection, that is, when the image reflects, the points remains fixed.

d. The line of reflection is perpendicular to the line segments connecting corresponding vertices. f. The line segments connecting corresponding vertices are all parallel to each other

If we reflect a figure across a vertical axis, the coordinates that change are the horizontal ones.

If we reflect a figure across a horizontal axis, the coordinates that change are the vertical ones.

So, in the first case, if we unit the initial horizontal coordinates with the reflected one, they are gonna be united with horizontal lines, and all of them are gonna be parallels and perpendicular to the line of reflection, which in this case is vertical. That's why d and f are also true.

answered: Guest

i think it might be a but you might want a second opinion