Question

On a coordinate grid, points Q and P represent positions of two midfield players. If P is 1.5 units to the left and 3 units down from the origin, and Q is 1.5 units to the left and 3 units up, what best describes their relationship?

a) Q is P reflected across the x-axis; only the signs of the x-coordinates of P and Q are different.
b) Q is P reflected across the x-axis; only the signs of the y-coordinates of P and Q are different.
c) Q is P reflected across the y-axis; only the signs of the x-coordinates of P and Q are different.
d) Q is P reflected across the y-axis; only the signs of the y-coordinates of P and Q are different.

Answer 1

Point Q is the reflection of point P across the x-axis because they have the same x-coordinates and y-coordinates of opposite signs.

Step-by-step explanation:

On a coordinate grid, when you have two points, P and Q, having specific positions, you can determine their relationship by looking at the coordinates of each point. Given that point P is 1.5 units to the left and 3 units down from the origin, its coordinates can be represented as (-1.5, -3). On the other hand, since point Q is 1.5 units to the left and 3 units up, its coordinates would be (-1.5, 3).

Comparing the coordinates of P and Q, we can see that the x-coordinates are identical (both -1.5), and the y-coordinates have the same numerical value but opposite signs. This demonstrates that point Q is the reflection of point P across the x-axis. This means that the correct answer to the relationship between P and Q is b) Q is P reflected across the x-axis; only the signs of the y-coordinates of P and Q are different.