Question

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Answer 1

If triangle UVW is dilated about the center of the triangle to create triangle U'V'W', dilated line A'B' will be parallel to AB.

Further explanation:

Given:

Triangle UVW is shown with point A lying on side UV and point B lying on side UW. Line AB is perpendicular to side UW.

Explanation:

If we dilate triangle UVW then the dilated triangle ${\text{U'V'W'}}$ is bigger than or smaller the triangle UVW.

The triangle UVW is similar to triangle ${\text{U'V'W'}}$ to each other.

The line ${\text{A'B'}}$ is perpendicular to the line {\text{U'W'}}.

So the line ${\text{A'B'}}$ is parallel to side AB.

If triangle UVW is dilated about the center of the triangle to create triangle U'V'W', dilated line A'B' will be parallel to AB.

Kindly refer to the image attached below.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: image vertices, AB, line, passing, point A, point B, triangle UVW, dilated, perpendicular to AB, lies, same line, shift four units, left, pre-imaged, dilation, center, scale factor, four, coordinates, x-coordinates, y-coordinate, transformation rule.

Answer 2

Answer:  AB will be parallel to A'B'.

Step-by-step explanation: We know the definition of dilation about the centre. It is defined as the enlargement or shrinken of the original figure keeping the centre of dilation or the figure as fixed.

We are given ΔUVW  and AB is perpendicular to UW. Now, if we dilate the triangle about the origin, then the triangle will either enlarge or shrink keeping the centre fixed.

Let us consider the enlarged triangle, ΔU'V'W' as shown in the attached figure. Also, line AB will move to the new position A'B'. We can clearly see that both the lines are parallel to each other.

Thus, the line segments AB and A'B' will be parallel too each other.