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) Answer: 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) Answer: 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) Answer: Third option (4,-9)
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.
