Answered

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Two transformations are applied to the triangle to create triangle L'M'N' so that MN and M'N' will both be parallel to the same axis, and LN and L’Nwill both be parallel to the same axis. Which pair oftransformations will not result in these corresponding sides of the two triangles being parallel to the sameaxis?

Two Transformations Are Applied To The Triangle To Create Triangle LMN So That MN And MN Will Both Be Parallel To The Same Axis And LN And LNwill Both Be Parall class=

Sagot :

Let us go through each of the choices one by one.

(a).

A rotation 90 degree clockwise followed by a translation 3 units down.

This Lands the L'M'N' into the first quadrant and L'N' is now parallel to the y-axis; therefore, this transformation leaves the corresponding sides not being parallel to the same axis and hence is the correct option to choose.

(b).

A translation 4 units to the left followed by a reflection over the y-axis.

A translation of 4 units to the left leaves the sides parallel and the reflection over the y-axis also leaves the sides parallel; therefore, this is not the correct option to choose.

(c).

A reflection over the x-axis followed by a dilation by a factor of 2 about the origin.

The reflection over the x-axis leaves the sides parallel and dilation by a factor of 2 just bloats the figure - it does not change the angle of sides with respect to the x and y axes; therefore, this choice is also not the correct one to choose.

(d).

A dilation by a factor of 0.25 about the origin followed by a 180° rotation clockwise about the origin.

The dilation by a factor of 0.25 shrinks the triangle, and the 180° rotation clockwise leaves the side L'M' parallel to the x-axis - the same as it was before; therefore, this is not the correct choice to choose.

Hence, the correct option is A.

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