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The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "RightArrow." For example: P(0, 0) RightArrow P′(1, 2).
Triangle ABC has coordinates
A
(
1
,
4
)
;
B
(
3
,
−
2
)
;
and
C
(
4
,
2
)
.
Find the coordinates of the image
A
'
B
'
C
'
after a reflection over the x-axis.
the x-coordinates stay the same
the y-coordinates change sign
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Enter your answer and show all the steps that you use to solve this problem in the space provided.
The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "RightArrow." For example: P(0, 0) RightArrow P′(1, 2).
Triangle ABC has coordinates
A(1,4);
B
(3−2);
and
C (4,2).
Find the coordinates of the image A'B'C' after a reflection over the x-axis.
To find the coordinates of the image points after a reflection over the x-axis, we need to change the sign of the y-coordinate while keeping the x-coordinate the same.
Let's start by finding the image point A'.
Since the reflection is over the x-axis, the x-coordinate of A' will be the same as the x-coordinate of A, which is 1.
To find the y-coordinate of A', we change the sign of the y-coordinate of A, which is 4. Changing the sign gives us -4.
Therefore, the coordinates of A' are (1, -4).
Now let's find the image point B'.
Again, the reflection is over the x-axis, so the x-coordinate of B' will be the same as the x-coordinate of B, which is 3.
To find the y-coordinate of B', we change the sign of the y-coordinate of B, which is -2. Changing the sign gives us 2.
Therefore, the coordinates of B' are (3, 2).
Finally, let's find the image point C'.
The x-coordinate of C' will be the same as the x-coordinate of C, which is 4.
To find the y-coordinate of C', we change the sign of the y-coordinate of C, which is 2. Changing the sign gives us -2.
Therefore, the coordinates of C' are (4, -2).
So, the coordinates of the image points after the reflection over the x-axis are:
A' (1, -4)
B' (3, 2)
C' (4, -2)