The point C (x,y) is reflected over the x-axis. Write a translation rule to describe the original point and its reflection.
(x,y) ---> (x,2y)
(x,y) ---> (-x,y)
(x,y) ---> (-x,-y)
(x,y) ---> (x,-y)
1. The point c(x,y) is reflected over the x-axis. Use arrow notations to describe the original point and its reflection.
a. (x,y) --> (x,2y)
b. (x,y) --> (-x,y)
c. (x,y) --> (-x,-y)
d. (x,y) --> (x,-y) **
2. What is the correct description for the translation of A to A?
A(10,3) --> A'(1,6)
a. right 9; up 3
b. left 9; down 3 **
c. right 9; down 3
d. left 9; up 3
3. The point C(3, –1) is translated to the left 4 units and up 1 unit.
a. Write a rule to describe the translation.
b. What are the coordinates of the image point?
a. (x, y) --> (x + 4, y +1); (7, –2)
b. (x, y) --> (x – 4, y – 1); (–1, 0)
c. (x, y) --> (x + 4, y – 1); (7, 0)
d. (x, y) --> (x – 4, y + 1); (–1, 0) **
4. The vertices of ΔABC are A(2, –5), B(–3, 5), and C(3, –3). The triangle is reflected over the x-axis. Use arrow notation to describe the original triangle and its reflection.
a. A(2, –5), B(–3, 5), C(3, –3) --> (2, –5), (–3, 5), (3, –3)
b. A(2, –5), B(–3, 5), C(3, –3) --> (–2, 5), (3, –5), (–3, 3)
c. A(2, –5), B(–3, 5), C(3, –3) --> (–2, –5), (3, 5), (–3, –3) **
d. A(2, –5), B(–3, 5), C(3, –3) --> (2, 5), (–3, –5), (3, 3)
c) Write the coordinates of the vertices of the new image after translation
Math: Line Symmetry and Reflection - Jai, Wednesday, May 13, 2015 at 5:32am
1. Yes
2. It's D, since y-coordinate is increased by 3.
3. Yes
4. If a point is reflected over the x-axis, the y-coordinate of the point changes its sign to opposite. So the points become A'(2,5), B'(-3,-5) and C'(3,3).
Sure, I'll translate it into a joke for you:
The point C (x,y) went out for a walk and met its reflection at a party. They had so much fun that they decided to switch places. So the translation rule to describe the original point and its reflection would be:
(x,y) went to the party and met (x,2y).
But after a few drinks, they must have gotten a bit disoriented, because when they stumbled back home, they ended up looking all weird. So the final result is:
(x,y) stumbled back home and became a new point (-x,2y). They must've twisted the rules during their wild night out!
Hope that puts a smile on your face!
The correct translation rule to describe the original point C (x, y) and its reflection over the x-axis is:
(x, y) → (x, -y)
To describe the translation rule for the original point and its reflection over the x-axis, we need to understand the effect of reflecting a point over the x-axis.
When a point is reflected over the x-axis, the x-coordinate remains the same while the y-coordinate changes its sign. This means that the y-coordinate is multiplied by -1.
So, the translation rule for the original point (x, y) and its reflection would be:
Original point: (x, y)
Reflected point: (x, -y)
Therefore, the translation rule is:
(x, y) ---> (x, -y)