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 first quadrant of the coordinate plane, since both its x and y coordinates are positive.
b) Applying the translation rule, we add 1 to the x-coordinate and subtract 5 from the y-coordinate of point A:
A’ = (4 + 1, 2 – 5) = (5, -3)
Point A’ is located in the fourth quadrant of the coordinate plane, since its x-coordinate is positive and its y-coordinate is negative.
c) To reflect A’ across the y-axis, we change the sign of its x-coordinate and leave the y-coordinate unchanged:
A’’ = (-5, -3)
Point A’’ is located in the third quadrant of the coordinate plane, since both its x and y coordinates are negative.
a) Point A(4, 2) is located in the first quadrant of the coordinate plane, because both x and y coordinates are positive.
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.
So, the translated coordinates of point A' would be:
x-coordinate: 4 + 1 = 5
y-coordinate: 2 - 5 = -3
Therefore, the coordinates of translated point A' are (5, -3). Point A' would be located in the fourth quadrant of the coordinate plane, because the x-coordinate is positive and the y-coordinate is negative.
c) To reflect point A' across the y-axis, we change the sign of the x-coordinate and keep the y-coordinate the same.
So, the coordinates of reflected point A'' would be:
x-coordinate: -5
y-coordinate: -3
Therefore, the coordinates of reflected point A'' are (-5, -3). Point A'' would still be located in the fourth quadrant of the coordinate plane, because the x-coordinate is negative and the y-coordinate is negative.
To answer these questions, we need to follow the given rules to find the coordinates of the points A’, and then find the coordinates of A’’ by reflecting A’ across the y-axis.
a) To determine the quadrant in which point A is located, we can observe the signs of its coordinates. The x-coordinate is positive (4), and the y-coordinate is positive (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 given translation rule. Adding 1 to the x-coordinate and subtracting 5 from the y-coordinate gives us:
x' = 4 + 1 = 5
y' = 2 - 5 = -3
The coordinates of translated point A’ are (5, -3). To determine the quadrant in which A’ is located, we observe the signs of its coordinates. The x-coordinate is positive (5), and the y-coordinate is negative (-3). Since the x-coordinate is positive and the y-coordinate is negative, A’ is located in the fourth quadrant of the coordinate plane.
c) To find the coordinates of reflected point A’’, we need to reflect A’ across the y-axis. Reflected points have their x-coordinate flipped in sign while the y-coordinate remains the same. Thus, the coordinates of A’’ are:
x'' = -5
y'' = -3
The coordinates of reflected point A’’ are (-5, -3). To determine the quadrant in which A’’ is located, we observe the signs of its coordinates. The x-coordinate is negative (-5), and the y-coordinate is negative (-3). Since both coordinates are negative, A’’ is located in the third quadrant of the coordinate plane.