Question

On a graph paper plot the triangle ABC whose vertices are at points A(5,4) , B(7,5) and C(-3,6). On the same graph , draw the image of the triangle ABC under reflection in the line y=3 . Mark any two points on the graph paper which are invariant under this reflection . Also , write the coordinates of points marked. ​

Answer 1

The coordinates of the points marked are (0,3) and (0,6)

To Find:

   Plot the triangle ABC on a graph paper using the given coordinates of its vertices A(5,4), B(7,5) and C(-3,6)

   Reflect the triangle ABC in the line y=3, by taking the coordinates of each point and reflecting them about the line y=3

   Connect the reflected points to form the reflected image of the triangle ABC

   Mark any two points on the graph paper which are invariant under this reflection

   Write the coordinates of the points marked.

Given:

The vertices of triangle ABC A(5,4), B(7,5) and C(-3,6)

The line of reflection y=3

To plot the triangle ABC on a graph paper and draw the image of the triangle ABC under reflection in the line y=3.

Solution:

To plot the triangle ABC on a graph paper, we need to first locate the points A(5,4), B(7,5) and C(-3,6) on the graph.

Point A is located at the coordinates (5,4), which means it is 5 units to the right of the y-axis and 4 units above the x-axis.

Point B is located at the coordinates (7,5), which means it is 7 units to the right of the y-axis and 5 units above the x-axis.

Point C is located at the coordinates (-3,6), which means it is 3 units to the left of the y-axis and 6 units above the x-axis.

To reflect the triangle ABC in the line y=3, we will take the coordinates of each point and reflect them about the line y=3. This means that the y-coordinate of each point will stay the same, but the x-coordinate will be multiplied by -1.

The reflected image of point A is A'(-5,4)

The reflected image of point B is B'(-7,5)

The reflected image of point C is C'(3,6)

Now we can connect these reflected points to form the reflected image of the triangle ABC.

Two points that are invariant under this reflection are the point of intersection of the line y = 3 and the x-axis, which is (0,3) and the point (0,6) which is a vertical distance of 3 units above the line of reflection.

The coordinates of the points marked are (0,3) and (0,6)

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