Identify triangleJIG right arrowtriangleDEF as a reflection, translation, rotation, or glide reflection. Find the reflection line, translation rule, center and angle of rotation, or glide translation rule and reflection line.
A coordinate grid shows both the x- and y-axes from -12 to 12 and the graphs of three triangles.
Triangle A B C has vertices
A at left parenthesis negative 9 comma 0 right parenthesis,
B at left parenthesis negative 6 comma negative 4 right parenthesis, and
C at left parenthesis negative 3 comma 0 right parenthesis.
Triangle D E F has vertices
D at left parenthesis negative 6 comma 8 right parenthesis,
E at left parenthesis negative 3 comma 8 right parenthesis, and
F at left parenthesis negative 3 comma 4 right parenthesis.
Triangle G H J has vertices
G at left parenthesis 5 comma 4 right parenthesis,
H at left parenthesis 2 comma 0 right parenthesis, and
J at left parenthesis 8 comma 0 right parenthesis.
A segment is drawn in the triangle from G to point I at 5 on the x axis creating two smaller triangles inside the larger triangle.
(1 point)
Responses
rotation; 180° about (1, 4)
rotation; 180° about (1, 4)
glide reflection; translate 8 units to the right then reflect across the line y = 4
glide reflection; translate 8 units to the right then reflect across the line y = 4
reflection; x = 5
reflection; x = 5
rotation; 180° about (–0.5, 0)
rotation; 180° about (–0.5, 0)
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Triangle JIG is a reflection.
The reflection line is the line x = 5.
Therefore, the correct answer is:
reflection; x = 5
To identify the transformation of triangle JIG -> triangle DEF, we can compare the coordinates of the vertices.
Triangle JIG has vertices:
J (-9, 0),
I (-6, 4), and
G (5, 4).
Triangle DEF has vertices:
D (-6, 8),
E (-3, 8), and
F (-3, 4).
By comparing the coordinates of the corresponding vertices, we can see that JIG has been reflected or flipped across the x-axis to form DEF. The reflection line is the x-axis.
Therefore, the transformation from triangle JIG to triangle DEF is a reflection across the x-axis.