ΔTRY if T(1, 2), R(4, 4) and Y(2, -3) is reflected in the x-axis then the y-axis. Find the coordinates of the new vertices. Type your new coordinates using proper notation.
*Hint: Copy and paste the below notASation for answer. All you need to do is replace the x,y with the appropriate points.
T''(x,y), R''(x,y), Y''(x,y)
When a point is reflected in the x-axis, the x-coordinate stays the same but the y-coordinate becomes its opposite. So, reflecting T(1, 2) in the x-axis gives T'(1, -2), reflecting R(4, 4) in the x-axis gives R'(4, -4), and reflecting Y(2, -3) in the x-axis gives Y'(2, 3).
When a point is then reflected in the y-axis, the y-coordinate stays the same but the x-coordinate becomes its opposite. So, reflecting T'(1, -2) in the y-axis gives T''(-1, -2), reflecting R'(4, -4) in the y-axis gives R''(-4, -4), and reflecting Y'(2, 3) in the y-axis gives Y''(-2, 3).
Therefore, the new vertices are T''(-1, -2), R''(-4, -4), and Y''(-2, 3).
Final Answer: T''(-1, -2), R''(-4, -4), and Y''(-2, 3)
Consider the pre-image triangle with vertices A(1,2), B(3,1), and C(1,1). Rotate the pre-image triangle ABC 90 degrees counterclockwise about the origin. Then, reflect the image over the x-axis.
*Hint: Copy and paste the below notASation for answer. All you need to do is replace the x,y with the appropriate points.
A''(x,y), B''(x,y), C''(x,y)
When a point is rotated 90 degrees counterclockwise about the origin, the new x-coordinate is equal to the original y-coordinate, and the new y-coordinate is the opposite of the original x-coordinate. So, rotated A is A'(-2,1), rotated B is B'(-1,-3), and rotated C is C'(-1,-1).
When a point is reflected over the x-axis, the x-coordinate stays the same but the y-coordinate becomes its opposite. So, reflecting A'(-2,1) gives A''(-2,-1), reflecting B'(-1,-3) gives B''(-1,3), and reflecting C'(-1,-1) gives C''(-1,1).
Therefore, the new vertices are A''(-2,-1), B''(-1,3), and C''(-1,1).
Final Answer: A''(-2,-1), B''(-1,3), and C''(-1,1).
To reflect a point in the x-axis, we only need to change the sign of the y-coordinate, while keeping the x-coordinate unchanged.
Let's start by reflecting the vertices T(1, 2), R(4, 4), and Y(2, -3) in the x-axis:
T' = (1, -2)
R' = (4, -4)
Y' = (2, 3)
Now, let's reflect these new vertices in the y-axis. To do this, we need to change the sign of the x-coordinate, while keeping the y-coordinate unchanged:
T'' = (-1, -2)
R'' = (-4, -4)
Y'' = (-2, 3)
Therefore, the new coordinates after reflecting the given vertices in both the x-axis and y-axis are:
T''(-1, -2), R''(-4, -4), Y''(-2, 3)