QuestionFind the new coordinates of point $N$ after dilating triangle $M N O$ by a factor of 3 from the origin, given $N(4,6)$ .

Studdy Solution

STEP 1

Assumptions1. The original coordinates of point N are (4,6) . The scale factor of dilation is33. The center of dilation is the origin (0,0)
4. Dilation is a transformation that alters the size of a figure without changing its shape or orientation. It multiplies all the coordinates of the original figure by the scale factor to get the coordinates of the dilated figure.

STEP 2

The formula for dilation with the origin as the center of dilation is given by $(x', y') = (kx, ky)$ where (x', y') are the coordinates of the point after dilation, (x, y) are the original coordinates of the point, and k is the scale factor.

STEP 3

Now, plug in the given values for the original coordinates of point N and the scale factor into the dilation formula.
$(x', y') = (3 \cdot,3 \cdot6)$

STEP 4

Calculate the new coordinates of point N.
$(x', y') = (12,18)$ So, the coordinates of point N in the dilated image are (12,18).

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