Question

Line AB contains point A(−4, 1) and point B (−1, 3). Find the coordinates of A′ and B′ after a dilation with a scale factor of 2 with a center point of dilation at the origin.

Answer 1

Explanation:

Step 1: Understanding the Dilation

A dilation with a scale factor of 2 and a center of dilation at the origin is a transformation that enlarges or shrinks an object by a factor of 2, with the origin (0, 0) as the center of the dilation.

Step 2: Using the Formula

To find the coordinates of the dilated points, we use the formula:

(x', y') = (2 * x, 2 * y)

Where (x, y) are the original coordinates of the points, and (x', y') are the coordinates of the dilated points.

Step 3: Finding the Coordinates of A′

We are given that the original coordinates of point A are (-4, 1), so we substitute these values into the formula:

A′ = (2 * -4, 2 * 1) = (-8, 2)

Step 4: Finding the Coordinates of B′

We are given that the original coordinates of point B are (-1, 3), so we substitute these values into the formula:

B′ = (2 * -1, 2 * 3) = (-2, 6)

Step 5: Conclusion

So, after a dilation with a scale factor of 2 and a center of dilation at the origin, the new coordinates of A′ and B′ are (-8, 2) and (-2, 6) respectively.

Answer 2

To find the coordinates of A′ and B′ after a dilation with a scale factor of 2 and with the center of dilation at the origin (0, 0), we need to apply the dilation formula:

(x', y') = (2 * (x - 0) + 0, 2 * (y - 0) + 0) = (2x, 2y)

For point A, the original coordinates are (-4, 1), so we substitute these values into the dilation formula:

(x', y') = (2 * (-4 - 0) + 0, 2 * (1 - 0) + 0) = (-8, 2)

So, after the dilation, the new coordinates of point A are (-8, 2).

For point B, the original coordinates are (-1, 3), so we substitute these values into the dilation formula:

(x', y') = (2 * (-1 - 0) + 0, 2 * (3 - 0) + 0) = (-2, 6)

So, after the dilation, the new coordinates of point B are (-2, 6).