26 points to whoever me on these 4 questions

2. Point P(x,y) reflected across the x-axis is P'(x,-y)
Then:
A(-6,-4)→A'(-6,-(-4))→A'(-6,4)
B(-3,5)→B'(-3,-5)
C(1,-1)→C'(1,-(-1))→C'(1,1)
First option A'(-6,4), B'(-3,-5), C'(1,1)

3. Point P(x,y) reflected across the y-axis is P'(-x,y)
Then:
P(-2,-4)→P'(-(-2),-4)→P'(2,-4)
Q(2,-5)→Q'(-2,-5)
R(-1,-8)→R'(-(-1),-8)→R'(1,-8)
Third option P'(2,-4), Q'(-2,-5), R'(1,-8)

4. Find the image of O(-2,-1) after two reflections, first across the line y=-5
O'(-2,-1-2(-1-(-5))=O'(-2,-1-2(-1+5))=O'(-2,-1-2(4))=O'(-2,-1-8)→O'(-2,-9)
And then across the line x=1
O''(-2+2(1-(-2),-9)=O''(-2+2(1+2),-9)=O''(-2+2(3),-9)=O''(-2+6,-9)=O''(4,-9)
Third option (4,-9)

5. Fourth option

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.

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.

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.

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.

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.