Question

Point D has coordinates of (−11,4). State the coordinates of the images D' and D" after R90 followed by rx​=−2. 1. Point D has coordinates of (−11,4). State the coordinates of the images D' and D" after R90 followed by rx​=−2.

Answer 1

After applying the transformations
`\( R_(90) \)` (rotation by 90 degrees) and
`\( r_x = -2 \)` to point D with coordinates (-11,4), the coordinates of the images are D'(-4,-11) and D''(-4,-11).

Step-by-step explanation:

To find the image coordinates after the rotation
`\( R_(90) \)`, we interchange the x and y coordinates and negate the new x-coordinate. For point D with coordinates (-11,4), after
`\( R_(90) \)`, the new coordinates are D' (4,-11).

Next, the reflection
`\( r_x = -2 \)` involves multiplying the x-coordinate by -1. For D' (4,-11), after
`\( r_x = -2 \)`, the new coordinates become D'' (-4,-11).

Understanding the properties of geometric transformations, such as rotations and reflections, allows us to apply these operations systematically to determine the final coordinates of the images. The process involves careful application of the transformation rules to each coordinate pair.

In summary, after rotating
`\( R_(90) \)` and reflecting
`\( r_x = -2 \)` from the original coordinates (-11,4), we obtain the final image coordinates D'(-4,-11) and D''(-4,-11).