Problem 1 :
The triangle PQR has the vertices P(1, 11), Q(1, 7) and R(3, 7).Reflect the triangle PQR across x-axis. Determine whether the triangle PQR and its reflected objects satisfy the above mentioned properties.
Problem 2 :
The triangle PQR has the vertices P(1, 11), Q(1, 7) and R(3, 7).Reflect the triangle PQR across y-axis. Determine whether the triangle PQR and its reflected objects satisfy the above mentioned properties.
1. Answer :
Step 1 :
Trace triangle PQR and the x- and y-axes onto a piece of paper.
Step 2 :
Fold the paper along the x-axis and trace the image of the triangle on the opposite side of the x-axis. Now, unfold the paper and label the vertices of the image P′, Q′ and R′.
Since the paper is folded along the x-axis, the line of reflection is x-axis.
Step 3 :
For the original figure, find the perpendicular distance from each point to the line of reflection.
From Point P to the line of reflection = 5 units
From Point Q to the line of reflection = 2 units
From Point R to the line of reflection = 2 units
Step 4 :
For the reflected figure, find the perpendicular distance from each point to the line of reflection.
From Point P' to the line of reflection = 5 units
From Point Q' to the line of reflection = 2 units
From Point R' to the line of reflection = 2 units
Step 5 :
From steps (3) and (4), it is clear that each point of the original figure PQR and its corresponding point on the image P'Q'R' must be at the same distance from the line of reflection.
Step 6 :
From step (5) it is clear that the triangle PQR and its reflected objects across x-axis satisfy the properties of reflection.
2. Answer :
Step 1 :
Trace triangle PQR and the x- and y-axes onto a piece of paper.
Step 2 :
Fold the paper along the y-axis and trace the image of the triangle on the left side of the y-axis. Now, unfold the paper and label the vertices of the image P", Q" and R".
Since the paper is folded along the y-axis, the line of reflection is y-axis.
Step 3 :
For the original figure, find the perpendicular distance from each point to the line of reflection.
From Point P to the line of reflection = 2 units
From Point Q to the line of reflection = 6 units
From Point R to the line of reflection = 2 units
Step 4 :
For the reflected figure, find the perpendicular distance from each point to the line of reflection.
From Point P" to the line of reflection = 2 units
From Point Q" to the line of reflection = 6 units
From Point R" to the line of reflection = 2 units
Step 5 :
From steps (3) and (4), it is clear that each point of the original figure PQR and its corresponding point on the image P"Q"R" must be at the same distance from the line of reflection.
Step 6 :
From step (5) it is clear that the triangle PQR and its reflected objects across y-axis satisfy the properties of reflection.
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