1) Question 2: The vertices of the triangle are A(-6, -4), B (-3,5), and C (1, - 1). Name the veritces of the image reflected across the x-axys.
Answer: first option A' (-6,4), B'(-3,-5), C'(1,1)
Explanation:
A reflection across the x-axis keeps the x-coordinate and takes the negative of the y-coordinate, i.e. (x,y) → (x,-y)
=> A (-6,-4) → A'(-6, 4)
B (-3,5) → B'(-3,-5)
C (1. - 1) → C'(1, 1)
2) Question 3: The vertices of the triangle are P(-2,-4), Q(2,-5), and R (-1,-8).Name the vertices of the image reflected across the y-axis.
Answer: third option: P'(2,-4), Q'(-2,-5), and R'(1,-8)
Explanation:
A reflection across the y-axis keeps the y-coordianate and takes the negative of the x-coordinate, i.e. (x,y) → (-x,y).
Therefore:
(-2,-4) → (2, -4)
(2, -5) → (-2, -5)
(-1, -8) → (1, -8)
3) Question 4: Find the image of O (-2,-1) after two reflections, first across the line y = - 5, and then across the line x = 1.
Answer: Third option (4, -9)
Explanation:
1) First reflection, across the line y = - 5.
That reflection keeps the x-coordinate and takes the y -coordinate a number of units down:
-1 - [ 4 + 4] = - 1 - 8 = - 9
The number 4 comes from the distance of the point (-2,-1) to the line y = - 5.
2) The second reflection, across the line x = 1.
That reflection keeps the y - coordinate and takes the x-coordinate a number of units to the left:
- 2 + [3 + 3] = - 2 + 6 = 4
The number 3 comes from the distance of the point (-2,-1) to the line x = 1.
4) Question 5. Which graph shows a triangle and its reflection image in the x-axis.
Answer: it is the last image, the fourth one.
Explanation:
It is like placing a mirror under the triangle (on the x-axis) and watching the reflection of the triangle.
Remember a reflection across the x-axis keeps the x-coordinate and taked the negative of the y-coordinate, i.e. (x,y) → (x, -y). You can check that this fits the last image.
