. 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 point A’? In which quadrant of the coordinate plane is point A’ located?
c) What are the coordinates of reflected point A’’? In which quadrant of the coordinate plane is point A’’ located?
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To determine the answers to the questions, let's follow these steps:
a) To find the quadrant of point A, we need to examine the signs of its coordinates. Point A(4, 2) has a positive x-coordinate and a positive y-coordinate. Hence, it is located in the first quadrant of the coordinate plane.
b) To translate point A according to the rule (x, y) → (x + 1, y – 5), we add 1 to the x-coordinate and subtract 5 from the y-coordinate. Therefore, the translated point A' will have the coordinates (4 + 1, 2 - 5) = (5, -3). Point A' has a positive x-coordinate and a negative y-coordinate, placing it in the fourth quadrant of the coordinate plane.
c) To reflect point A' across the y-axis, we just negate the x-coordinate without altering the y-coordinate. Thus, the reflected point A'' will have the coordinates (-5, -3). Point A'' has a negative x-coordinate and a negative y-coordinate, indicating that it is located in the third quadrant of the coordinate plane.
In summary:
a) Point A is located in the first quadrant of the coordinate plane.
b) The translated point A' has coordinates (5, -3) and is located in the fourth quadrant of the coordinate plane.
c) The reflected point A'' has coordinates (-5, -3) and is located in the third quadrant of the coordinate plane.