Question

Square LMNO is on the coordinate plane.

point O is (1, 4)

Point L is (1, 2)

Point N is (3, 4)

Point M is (3, 2)

The square is dilated by a scale factor of 4 with respect to the origin. What will be the coordinates of square L'M'N'O'?

Answer 1

To find the coordinates of square L'M'N'O' after it is dilated by a scale factor of 4 with respect to the origin, we will apply the dilation formula for each vertex of square LMNO.

The dilation formula for a point \((x, y)\) with respect to the origin with scale factor \(k\) is given by:
\[
(x', y') = (kx, ky)
\]

Given the original vertices of square LMNO:
- Point O: \((1, 4)\)
- Point L: \((1, 2)\)
- Point N: \((3, 4)\)
- Point M: \((3, 2)\)

We will apply the dilation for each of these points with a scale factor of \(4\).

1. For point O \((1, 4)\):
\[
O' = (4 \cdot 1, 4 \cdot 4) = (4, 16)
\]

2. For point L \((1, 2)\):
\[
L' = (4 \cdot 1, 4 \cdot 2) = (4, 8)
\]

3. For point N \((3, 4)\):
\[
N' = (4 \cdot 3, 4 \cdot 4) = (12, 16)
\]

4. For point M \((3, 2)\):
\[
M' = (4 \cdot 3, 4 \cdot 2) = (12, 8)
\]

Thus, the new coordinates of the vertices of the dilated square L'M'N'O' are:
- L' = \((4, 8)\)
- M' = \((12, 8)\)
- N' = \((12, 16)\)
- O' = \((4, 16)\)

So, the coordinates of square L'M'N'O' after the dilation are:
- L' = (4, 8)
- M' = (12, 8)
- N' = (12, 16)
- O' = (4, 16)