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Chapter 1: Q 90 (page 25)

Open the origin symmetry applet. Move point A around the Cartesian plane with your mouse. How are the coordinates of point A and the coordinates of point B related?

Short Answer

Expert verified

IfAx,ythenB-x,-y

Step by step solution

01

Step 1. Given information

Open the origin symmetry applet. Move point A around the Cartesian plane with your mouse.

02

Step 2. Relation between the coordinates

If point A moves from the origin then point B also moves away because the distance of point B and point A to the origin are equal.

03

Step 3. 

The x and y coordinates of points A and B are opposite values, therefore the conclusion is the same if we move point A along the other quadrants

Point B which is axisymmetric to point Ax,ywith respect to y-axis has coordinatesB-x,-y

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Most popular questions from this chapter

Microphones In studiosand on stages, cardioid microphones are often preferred for the richness they add to voices and for their ability to reduce the level of sound from the sides and rear of the microphone. Suppose one such cardioid pattern is given by the equation x2+y2-x2=x2+y2
.

(a) Find the intercepts of the graph of the equation.

(b) Test for symmetry with respect to the x-axis, y-axis, and origin.

In Problems 70, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.

y=x2-8

x3-4x+2=0

Plot each point. Then plot the point that is symmetric to it with respect to -

(a) the x-axis

(b) the y-axis

(c) the origin

Point (3, 4)

True or False The point (-1,4)lies in quadrant IV of the Cartesian plane.
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