A line containing the points (−2, 3) and (2, 3) is reflected across the x -axis. How long is the reflected line?
When a line is reflected across the x-axis, the y-coordinates of the points are negated.
The reflected y-coordinate of (-2, 3) is -3.
The reflected y-coordinate of (2, 3) is also -3.
The distance between two points with the same y-coordinate is just the absolute value of the difference in their x-coordinates.
So, the length of the reflected line is |(-2) - 2| = 4 units.
A line segment has endpoints (2,−1) and (5, −4) . What are the new endpoints after rotating the segment 90° clockwise?
To rotate a point 90° clockwise, we need to swap the x and y coordinates and negate the new y coordinate.
For the first endpoint (2, -1):
- The new x-coordinate is the negative of the original y-coordinate: -(-1) = 1.
- The new y-coordinate is the original x-coordinate: 2.
So the new coordinates for the first endpoint are (1, 2).
For the second endpoint (5, -4):
- The new x-coordinate is the negative of the original y-coordinate: -(-4) = 4.
- The new y-coordinate is the original x-coordinate: 5.
So the new coordinates for the second endpoint are (4, 5).
A rectangle has a side that is 10 units long. How long will this side be after the figure is translated down 4 units and to the right 5 units?
After translating the rectangle down 4 units, the length of the side will remain the same.
After translating the rectangle to the right 5 units, the length of the side will still be 10 units, as translation does not change the length of the sides of a shape.
So, the length of the side of the rectangle will still be 10 units.