REFLECTIONS - Advanced Pre-Calculus
Review:
Rule for X-Axis Reflection Equation for X-Axis Reflection
(x,y) ( (x,-y) x’ = x and y’ = -y
When Reflecting:
The reflection of a line is a _________________.
The reflection of a segment is a ____________________.
After reflection, the size and shape of the object are ___________.
Reflections over y = x and y = -x
Reflect [pic] over the line y = x. Reflect [pic] over y = - x.
P(3, -1) and Q (4, -3) p (2, -7) and Q ( 6, -5)
Examples
Graph [pic] using the points A(-4, 1) and B(4,7) and graph the image after a reflection in the y-axis.
Find the slope of [pic]___________.
Find the slope of [pic] ________.
How are these slopes related?
Write the equation of the line that contains AB and A’ and B’. What do you notice about the y-intercepts? Would this also happen if the reflection had been in the x-axis
9-2 Reflections Worksheet NAME ________________Date ____
For exercises 1-4 a transformation is specified by the equations:
x( = -x and y( = y
1. Describe the transformation verbally.
2. Point (-3,5) has what image?
3. Point (2,-9) has what preimage?
4. Describe the set of all fixed points under the transformation.
State the equation of the reflection that maps the first point into the second point and describe the transformation.
5. (7,4) ( (7,-4) 6. (-3,2) ( (3,2)
1. (0,2) ( (0,2) 8. (a,4) ( (a,-4)
In exercises 9-12, draw [pic] and its image, [pic], after reflection over the x-axis.. Find the length of [pic] and [pic]. Find the slope of [pic] and [pic]. Write the equations for the lines containing [pic] and [pic].
9. P(-1,2), Q(5,2) 10. P(-2,0), Q(-2,4) 11. P(0,1), Q(3,5)
|PQ = | | | |
|P’Q’ = | | | |
|m[pic] = | | | |
|m[pic] = | | | |
|Slope intercept equation of| | | |
|[pic] | | | |
|Slope intercept equation of| | | |
|[pic] | | | |
12. (a) What is the relationship between PQ and P’Q’?
(b) What is the relationship between the slopes of [pic] and [pic]?
In exercises 13-15, plot points A, B, and C. Draw triangle ABC. On the same coordinate grid draw the image of triangle ABC after a reflection over the line indicated.
13. A(1,-1), B(1,3), C(4,4) 14. A(3,4), B(-2,6), C(-5,5) 15. A(1,3), B(0,6), C(-3, 2)
over the y-axis over the x-axis over y = x
In exercises 16-19, you are given point P(1,1), Q(2,3), and R(4,7). Use the reflection over the x-axis to find the images of points P, Q, and R.
16. State the slope of [pic]. ________ and of [pic]. __________. Are points P, Q, and R collinear? ______ (Note: three points are collinear if the slopes are the same. The segments cannot be parallel since they have a point in common.)
17. State the coordinates of point P(________, Q(_________, and R(_________. State the slope of [pic] __________, of [pic] _________. Are points P’, Q’, and R’ collinear? __________
18. What can you conclude about the reflection of a set of collinear points?
19. Reflect [pic]over y = x. 20. Reflect [pic]over y = - x.
T( -7, -1) W(-2, 3) T(-5, 2) W(2, -4)
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