Question

ab is a translation of cd. to the nearest tenth, what is the length of each segment? explain the effect of a translation on the length of a line segment
a ab is about 11.5 units. cd is about 10 units. a translated segment is longer than the original segment
b ab is about 10.5 units. cd is about 11.5 units. a translated segment is shorter than the original segment
c ab is about 11.3 units. cd is about 11.3 units. the length of a translated segment is the same as the original segment
d ab is about 12.5 units. cd is about 12.5 units. the length of a translated segment is the same as the original segment

Explanation:

Step1: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For segment \(\overline{AB}\), assume \(A(x_1,y_1)\) and \(B(x_2,y_2)\). Count the horizontal and vertical distances. Suppose the horizontal change \(\Delta x\) and vertical change \(\Delta y\). If \(\Delta x = 5\) and \(\Delta y = 10\) (by counting grid - squares), then \(d_{AB}=\sqrt{5^{2}+10^{2}}=\sqrt{25 + 100}=\sqrt{125}\approx11.2\). For segment \(\overline{CD}\), since translation is a rigid transformation (a transformation that preserves distances and angles). A translation moves every point of a figure or space by the same distance in a given direction. So the length of \(\overline{CD}\) is the same as the length of \(\overline{AB}\).

Answer:

C. \(\overline{AB}\) is about \(11.3\) units; \(\overline{CD}\) is about \(11.3\) units. The length of a translated segment is the same as the original segment.