Question

8th grade math geometry
problem 4: explain why translations preserve segment length but dilations (k≠1) do not.
answer:
problem 5: draw a segment and reflect across y - axis. measure original and image.
reflect △abc across x - axis
answer:

Explanation:

Problem 4

A translation is a rigid - motion that slides every point of a figure the same distance in the same direction. It does not change the shape or size of the figure, so segment lengths are preserved. A dilation with a scale factor \(k
eq1\) multiplies the distance between points by \(k\). If \(|k|> 1\), segments get longer; if \(0 < |k|<1\), segments get shorter.

1. Use a straight - edge to draw a line segment on the coordinate plane. Let's say the endpoints of the segment are \((x_1,y_1)\) and \((x_2,y_2)\).
2. To reflect a point \((x,y)\) across the \(y\) - axis, the new point is \((-x,y)\). So, find the reflected endpoints of the segment.
3. Use a ruler to measure the length of the original segment and the length of the reflected segment. You will find they are equal because reflections across an axis are rigid - motions.
4. To reflect \(\triangle ABC\) across the \(x\) - axis, for a point \((x,y)\) in \(\triangle ABC\), the new point is \((x, - y)\). Plot the new points for the vertices of the triangle.

Answer:

Translations are rigid - motions that do not change distances between points, so segment lengths are preserved. Dilations with \(k
eq1\) change distances between points by multiplying them by the scale factor \(k\), so segment lengths are not preserved.

Problem 5