Point A(4, 2) is translated according to the rule (x, y) (x + 1, y - 5) and then reflected across the y-axis.
A) In which quadrant of the coordinate plane is point A located.
B) What are the coordinates of translated points A'? In which quadrant plane is point A located?
C) What are the coordinates of reflected point A? In which quadrant plane is point A located?
I know for the first part that point A is located in the 1st quadrant the rest I have no idea.
Please I need help
to translate, (4,2) -> (4+1,2-5) = (5,-3)
Now reflect that across the y-axis, and (5,-3) -> (-5,-3)
Thank you so much!!!!
It’s the practice
To solve parts B and C, we will perform the given translations and reflections step by step.
A) Since point A(4, 2) has positive coordinates in both the x and y-axis, it is originally located in the first quadrant.
B) To find the coordinates of translated point A' after the given translation rule (x, y) -> (x + 1, y - 5), we apply the rule to each coordinate of A:
x-coordinate of A': x-coordinate of A + 1 = 4 + 1 = 5
y-coordinate of A': y-coordinate of A - 5 = 2 - 5 = -3
Hence, point A' has the coordinates (5, -3).
To determine the quadrant in which point A' is located, we examine the signs of its x and y-coordinates.
The x-coordinate of A' is positive, and the y-coordinate of A' is negative. Therefore, A' is located in the fourth quadrant.
C) Now, let's reflect point A' across the y-axis to find the coordinates of the reflected point. Reflecting a point across the y-axis simply means changing the sign of its x-coordinate while keeping the y-coordinate constant.
Reflected x-coordinate of A: -5
Y-coordinate of A remains -3.
So, the coordinates of the reflected point A after reflection are (-5, -3).
To determine the quadrant in which the reflected point A is located, we examine the signs of its x and y-coordinates.
The x-coordinate of A is negative, and the y-coordinate of A is negative. Therefore, the reflected point A is located in the third quadrant.
To summarize:
A) Point A is located in the first quadrant.
B) The coordinates of translated point A' are (5, -3), and it is located in the fourth quadrant.
C) The coordinates of the reflected point A are (-5, -3), and it is located in the third quadrant.