If the point P(-3,2) is translated under the vector (1,-5) what quadrant will P' be located?
Quadrant 3?
P' = (-3,2) + (1,-5)
= .....
To determine the quadrant where the point P' will be located after being translated, we need to understand how the translation works.
A translation involves adding the components of a vector to the coordinates of a point. In this case, the vector is (1, -5), which means we are adding 1 to the x-coordinate and -5 to the y-coordinate.
Let's calculate the coordinates of P' after the translation:
x-coordinate of P': -3 + 1 = -2
y-coordinate of P': 2 - 5 = -3
The coordinates of P' are (-2, -3).
To determine the quadrant, we look at the signs of the x and y coordinates. If both coordinates are positive, the point is in Quadrant 1. If the x-coordinate is negative and the y-coordinate is positive, the point is in Quadrant 2. If both coordinates are negative, the point is in Quadrant 3. If the x-coordinate is positive and the y-coordinate is negative, the point is in Quadrant 4.
In this case, the x-coordinate (-2) is negative, and the y-coordinate (-3) is also negative. Therefore, the point P' is located in Quadrant 3.