Question

1 in the graph below, △e’f’g’ is the image produced by applying a transformation to △efg. which rule describes the transformation? a. ((x, y) = (-x, y)) b. ((x, y) = (y, -x)) c. ((x, y) = (x, -y)) d. ((x, y) = (-y, x)) 1 in this diagram, (overline{lm} cong overline{op}) and (overline{lp} cong overline{om}). which statement is needed to prove (\triangle lmp cong \triangle opm) by sss? a. (overline{lm} cong overline{lp}); reflexive property b. (overline{mp} cong overline{pm}); reflexive property c. (overline{lm} cong overline{lp}); symmetric property d. (overline{mp} cong overline{pm}); symmetric property

Explanation:

First Sub - Question (Triangle Transformation)

Step1: Identify Coordinates

Let's take a point from \(\triangle EFG\), say \(E\). From the graph, \(E\) has coordinates \((2,2)\). The corresponding point \(E'\) in \(\triangle E'F'G'\) has coordinates \((2, - 2)\).

Step2: Analyze Transformation

For a point \((x,y)\) and its image \((x',y')\), we see that \(x'=x\) (since \(2 = 2\)) and \(y'=-y\) (since \(- 2=-2\)). So the transformation rule is \((x',y')=(x, - y)\).

Step1: Recall SSS Congruence

To prove \(\triangle LMP\cong\triangle OPM\) by SSS, we need three pairs of congruent sides. We know \(\overline{LM}\cong\overline{OP}\) and \(\overline{LP}\cong\overline{OM}\) (given). The third pair should be the common side \(\overline{MP}\) and \(\overline{PM}\).

Step2: Identify Property

The reflexive property states that a segment is congruent to itself, so \(\overline{MP}\cong\overline{PM}\) by the reflexive property.

Answer:

C. \((x',y')=(x, - y)\)

Second Sub - Question (Triangle Congruence by SSS)