Reflections Across the x- or y- Axis Practice

Question

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Question
Use the image to answer the question.

An illustration shows a coordinate plane. The x-axis and the y-axis range from negative 6 to 6 in one unit increments. Six points are plotted on the plane. Two right triangles are graphed on the plane. Three points are plotted in the first quadrant. Point A is plotted at the coordinates left parenthesis 3 comma 2 right parenthesis, Point B is plotted at left parenthesis 3 comma 6 right parenthesis, and point C is plotted at left parenthesis 6 comma 2 right parenthesis. Points A and B, points B and C, and points C and A are connected by a dotted line segment to form triangle A B C. Three points are plotted in the second quadrant. Point D is plotted at the coordinates left parenthesis negative 3 comma 2 right parenthesis, Point E is plotted at left parenthesis negative 3 comma 6 right parenthesis, and point F is plotted at left parenthesis negative 6 comma 2 right parenthesis. Points D and E, points E and F, and points F and D are connected by line segments to form triangle D E F.

Triangle ABC
is reflected across the y
-axis to produce triangle DEF
. Which segment on DEF
is congruent to the segment BC
?

(1 point)
segment

Answer 1

To determine which segment on triangle DEF is congruent to segment BC from triangle ABC after reflecting across the y-axis, we first need to identify the coordinates of points in both triangles.

For triangle ABC:

• Point A: (3, 2)
• Point B: (3, 6)
• Point C: (6, 2)

For triangle DEF, which is the reflection of triangle ABC across the y-axis:

• Point D: (-3, 2) (reflecting A)
• Point E: (-3, 6) (reflecting B)
• Point F: (-6, 2) (reflecting C)

Now we identify segment BC on triangle ABC:

• Segment BC connects points B (3, 6) and C (6, 2).

Next, we calculate the coordinates of segment EF on triangle DEF:

• Segment EF connects points E (-3, 6) and F (-6, 2).

Now, let's see if the lengths of segments BC and EF are equal:

Length of segment BC: \[ \text{Length of BC} = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} = \sqrt{(6 - 3)^2 + (2 - 6)^2} = \sqrt{(3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

Length of segment EF: \[ \text{Length of EF} = \sqrt{(x_F - x_E)^2 + (y_F - y_E)^2} = \sqrt{(-6 - (-3))^2 + (2 - 6)^2} = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

Since both segments have the same length, the segment on triangle DEF that is congruent to segment BC is segment EF.

Therefore, the answer is:

segment EF