Question

is ijk congruent to tuv? justify your answer. yes, because a translation left 10 units and down 1 unit maps ijk onto tuv. yes, because a reflection across the y - axis maps ijk onto tuv. no, because ∠k and ∠v do not have the same measure. no, because ij and tu do not have the same length.

Explanation:

Step1: Calculate the length of \( IJ \) and \( TU \)

Use the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
For \( IJ \): Let \( I=(8,-4) \), \( J=(3,-7) \).
\( d_{IJ}=\sqrt{(8 - 3)^2+(-4+7)^2}=\sqrt{25 + 9}=\sqrt{34} \).
For \( TU \): Let \( T=(-2,-6) \), \( U=(-7,-8) \).
\( d_{TU}=\sqrt{(-2 + 7)^2+(-6 + 8)^2}=\sqrt{25+4}=\sqrt{29} \).

Answer:

No, because \( \overline{IJ} \) and \( \overline{TU} \) do not have the same length.