Question

Graph the image of the given triangle under a dilation with a scale factor of 1/3 and center of dilation (0, 0) .

To graph the triangle, select the "Polygon" tool and draw the triangle by plotting each vertex in order until it lands back on the first vertex. Do not retrace any sides. You may use the "Move" tool to move your image if you needed.

Answer 1

We are given : A scale factor of 1/3 and center of dilation (0, 0).

For the given image, the coordinates of the vertices of the triangle are

(0,9), (0,0) and (-6,0).

We can apply formula for finding new coordinates:

Scale factor * [Vertex coordinates of the given image - Coordinate of Center of dilation] +Coordinate of Center of dilation.

Applying same formula to each coordinates we are given.

(0,9) --> 1/3 [ (0,9) - (0,0) ] + (0,0) ] = 1/3 [ (0,9)] +(0,0) = (0,3).

(0,0) --> 1/3 [ (0,0) - (0,0) ] + (0,0) ] = 1/3 [ (0,0] +(0,0) = (0,0).

(0,9) --> 1/3 [ (-6,0) - (0,0) ] + (0,0) ] = 1/3 [ (-6,0)] +(0,0) = (-2,0).

Now, we can plot those resulting coordinates on the graph and form a triangle.