On the graph at right, plot, label, and connec in order the following points.

A(-4,-1) B(-1,-3) C(-6,-2)

a) Reflect ABC across the x-axis. Label the new triangle A'B'C.\

b) Are ABC and A'B'C similar? Explain completely, justifying your answer.

c) Multiply each coordinate of ABC by -1, and plot the new triangle, labeling it XYZ. Is XYZ a translation(slide), rotation(turn), reflection(flip) or dilation of ABC? Explain how you know.

d) Multiply each coordinate of ABC by -2, and plot the new triangle, labeling it PQR. Is PQR similar to the original ABC? Explain why or why not, being clear and complete

waffles
May 22, 2017

#1**+2 **

Even though I have not graphed these triangles, knowing the relationships is enough to answer these questions with sufficient justification:

a) When reflecting points over the x-axis, the following rule applies to all transformed points:

(x,y)--->(x,-y)

What this means is that the x-coordinate remains unchanged, but the y-coordinate changes to its opposite. Therefore, the coordinates of the new triangle is:

A'(-4,1), B'(-1,3), and C'(-6,2)

b) Yes, \(\triangle\)ABC and \(\triangle\)A'B'C' are similar. In fact, it is an isometry (congruent transformation). This is because a reflection is merely a mirror image of the pre-image.

c) For this tranformation, the rule is as follows:

(x,y)-->(-x,-y)

Therefore, the resulting coordinates become:

X(4,1), Y(1,3), Z(6,2)

Also, this transformation is the equivalent of a rotation about the origin 180 degrees counterclockwise. We know this because if the scale factor, k,<0 then it always results in a rotation.

d) Triangle PQR is similar to Triangle ABC because multiplying the coordinates by any scale factor always results in similar figures.

TheXSquaredFactor
May 23, 2017

#1**+2 **

Best Answer

Even though I have not graphed these triangles, knowing the relationships is enough to answer these questions with sufficient justification:

a) When reflecting points over the x-axis, the following rule applies to all transformed points:

(x,y)--->(x,-y)

What this means is that the x-coordinate remains unchanged, but the y-coordinate changes to its opposite. Therefore, the coordinates of the new triangle is:

A'(-4,1), B'(-1,3), and C'(-6,2)

b) Yes, \(\triangle\)ABC and \(\triangle\)A'B'C' are similar. In fact, it is an isometry (congruent transformation). This is because a reflection is merely a mirror image of the pre-image.

c) For this tranformation, the rule is as follows:

(x,y)-->(-x,-y)

Therefore, the resulting coordinates become:

X(4,1), Y(1,3), Z(6,2)

Also, this transformation is the equivalent of a rotation about the origin 180 degrees counterclockwise. We know this because if the scale factor, k,<0 then it always results in a rotation.

d) Triangle PQR is similar to Triangle ABC because multiplying the coordinates by any scale factor always results in similar figures.

TheXSquaredFactor
May 23, 2017