Note: For questions 19 and 20, your teacher will grade your response to ensure you receive proper credit for your answer.
Point A(4, 2) is translated according to the rule (x, y) right arrow (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?
a) Point A is located in the second quadrant of the coordinate plane.
b) The coordinates of translated point A’ are (5, -3). Point A’ is located in the fourth quadrant of the coordinate plane.
c) The coordinates of reflected point A’’ are (5, 3). Point A’’ is located in the second quadrant of the coordinate plane.
a) To determine the quadrant in which point A is located, we need to analyze the signs of its x and y coordinates. Point A has x-coordinate 4 and y-coordinate 2. Since both coordinates are positive, point A is located in the first quadrant of the coordinate plane.
b) To find the coordinates of translated point A', we apply the translation rule (x, y) -> (x + 1, y - 5) to the coordinates of A.
For the x-coordinate:
x' = x + 1 = 4 + 1 = 5.
For the y-coordinate:
y' = y - 5 = 2 - 5 = -3.
Therefore, the coordinates of translated point A' are (5, -3). Since the x-coordinate is positive and the y-coordinate is negative, point A' is located in the fourth quadrant of the coordinate plane.
c) To find the coordinates of reflected point A'', we need to reflect the coordinates of A' across the y-axis.
To reflect a point across the y-axis, we change the sign of its x-coordinate while keeping the y-coordinate the same.
For the x-coordinate:
x'' = -x' = -(5) = -5.
For the y-coordinate:
y'' = y' = -3.
Therefore, the coordinates of reflected point A'' are (-5, -3). Since both coordinates are negative, point A'' is located in the third quadrant of the coordinate plane.
a) Point A(4, 2) is located in the first quadrant of the coordinate plane.
b) The translation rule (x, y) right arrow (x + 1, y – 5) will move the point A(4, 2) one unit to the right and 5 units down. Therefore, the translated point A' will have coordinates (5, -3). Point A' is located in the fourth quadrant of the coordinate plane.
c) Reflecting the point A' across the y-axis will change the sign of the x-coordinate. Therefore, the coordinates of the reflected point A'' will be (-5, -3). Point A'' is located in the second quadrant of the coordinate plane.