Question

the graph shows triangles ijk and tuv. 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 (overline{ij}) and (overline{tu}) do not have the same length.

Explanation:

Step1: Calculate the length of \( IJ \)

Use the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
For points \( I(8,-5) \) and \( J(2,-7) \), \( IJ=\sqrt{(8 - 2)^2+(-5+7)^2}=\sqrt{36 + 4}=\sqrt{40} = 2\sqrt{10} \).

Step2: Calculate the length of \( TU \)

For points \( T(-2,-6) \) and \( U(-6,-8) \), \( TU=\sqrt{(-2 + 6)^2+(-6 + 8)^2}=\sqrt{16+4}=\sqrt{20}=2\sqrt{5} \).
Since \( IJ
eq TU \), the triangles are not congruent.

Answer:

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