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Graph the image of the given triangle under a dilation with a scale factor of 14 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 needed.

The imagine, that is on the graph is. (0,4) (0,0) (8,0)

1 answer

To graph the image of the triangle under a dilation with a scale factor of 14 and a center of dilation at (0, 0), you'll need to follow these steps:

  1. Identify the original vertices of the triangle:

    • The vertices of the original triangle are:
      • A(0, 4)
      • B(0, 0)
      • C(8, 0)

  2. Apply the dilation formula: The formula for dilation is: \[ (x', y') = (k \cdot x, k \cdot y) \] where \( (x, y) \) are the coordinates of the original points and \( k \) is the scale factor.

    For a scale factor of \( k = 14 \):

    • For point A(0, 4): \[ A' = (14 \cdot 0, 14 \cdot 4) = (0, 56) \]
    • For point B(0, 0): \[ B' = (14 \cdot 0, 14 \cdot 0) = (0, 0) \]
    • For point C(8, 0): \[ C' = (14 \cdot 8, 14 \cdot 0) = (112, 0) \]

  3. List the coordinates of the dilated triangle: The coordinates of the vertices of the dilated triangle are:

    • A'(0, 56)
    • B'(0, 0)
    • C'(112, 0)

  4. Graph the new triangle:

    • Use the "Polygon" tool.
    • Plot the new vertices in order:
      • Start at A' (0, 56)
      • Draw a line to B' (0, 0)
      • Draw a line to C' (112, 0)
      • Finally, close the polygon by connecting back to A' (0, 56).

  5. Check your work: Make sure that the triangle is accurately plotted and that it does not retrace any sides.

By following these steps, you should be able to graph the dilated triangle accurately.