Which set of reflections would carry rectangle ABCD onto itself?
2 answers:
Answer with explanation:
The coordinates of vertices of Rectangle A B CD which lies in first Quadrant
=A(1,1),B(1,3),C(4,3) and D(4,1).
We have to find set of reflections which will carry rectangle ABCD onto itself.
Option-1:
When we reflect the rectangle along y axis,the rectangle moves in second Quadrant,and when it is reflected through x axis,it goes in Third Quadrant,and when it is reflected through y axis, the rectangle get transferred into fourth quadrant.This set of reflection would not carry rectangle ABCD onto itself.
Option-2:
When we reflect the rectangle along x axis,the rectangle moves in fourth Quadrant, and when it is reflected through y axis,it goes in Third Quadrant,and when it is reflected through y axis, the rectangle get transferred into fourth quadrant.This set of reflection would not carry rectangle ABCD onto itself.
Option-3
When we reflect the rectangle through x axis, the rectangle moves in fourth quadrant, having vertices A(1,-1),B(1, -3),C(4,-3) and D(4,-1).And when it is reflected through line y=x,the coordinates of rectangle becomes which goes into second quadrant A(-1,1),B(-3,1),C(-3,4) and D(-1,4).Now when the rectangle is reflected through x axis it moves into third Quadrant having vertices A(-1,-1),B(-3,-1),C(-3,-4) and D(-1,-4).Reflecting the rectangle along line , y=x takes it to third Quadrant having vertices A(-1,-1),B(-1,-3),C(-4,-3) and D(-4,-1).This set of reflection would not carry rectangle ABCD onto itself.
Option-4
Reflecting the rectangle along line , y=x gives the vertices of reflected rectangle A(1,1),B(3,1),C(3,4) and D(1,4).Now reflecting this rectangle through x axis takes it to fourth Quadrant having Vertices A(1,-1),B(3,-1),C(3,-4) and D(1,-4).Then reflecting through ,y=x ,takes this rectangle to A(-1,1),B(-1,3),C(-4,3) and D(-4,1),that is into second quadrant.Then reflecting through y axis, takes it to first Quadrant.So, This set of reflection would carry rectangle ABCD onto itself.
Option D:⇒ y=x, x-axis, y=x, y-axis
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Answer:
Domain: {-3, 0 3}
Range: {0, 3}
Step-by-step explanation:
Recall that the Domain of a relationship associated with coordinate pairs of the form (x,y), is the set of all "x-values" given in the relationship.
The Range is the set of all "y-values" given in the relationship.
In our case, we have three coordinate points defining the relationship. These points have the following (x,y) coordinates (see attached image to see which coordinates are associated with each point):
(-3, 3), (0, 0), and (3, 3)
Therefore, the x values associated with these points are: -3, 0 and 3
therefore the Domain of the relationship is the set: { -3, 0, 3}
On the other hand, he y values associated with these points are: 3, 0, and again 3. So in fact there are just to distinct y-values: 0 and 3.
therefore the Range of the relationship is he set: {0, 3}
which corresponds to answer B.
