A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4)?
A) a reflection of the line segment across the x-axis
B)a reflection of the line segment across the y-axis
C)a reflection of the line segment across the line y = x
D)a reflection of the line segment across the line y = –x
Answers
Answer:
Reflection about the line segment across y axis
Step-by-step explanation:
Since we can see that the y coordinate remains the same after reflection and the x coordinate reverse it sign after reflection , it should be the reflection about the y axis
Reflection about y axis= before (x,y) after (-x,y)
about x axis = before (x,y) after(x,-y)
about y=x = before(x,y) after (y,x)
about y=-x before(x,y) after(-y,-x)
Answer:
B) a reflection of the line segment across the y-axis.
Step-by-step explanation:
Given:- Given co-ordinates are (-4, -6) and (-6, 4).
To Find:- Across which axis the given line segment will produce an image with endpoints (4, -6) and (6, 4).
Solution:-
As we know, in a 2-dimensional graph, x-axis and y-axis form 4 quadrants.
In the 1st quadrant, x and y is positive.
In 2nd quadrant, x is negative where as y is positive.
In 3rd quadrant, x and y both are negative.
In 4th quadrant, x is positive whereas y is negative.
Our point (-4, -6) lies in 3rd quadrant. So (4, -6) will be produced with it's reflection across y-axis as (4, -6) lies in 4th quadrant.
(-6, 4) lies in 2nd quadrant and it will produce a reflection of (6, 4) across y-axis as (6, 4) lies in 1st quadrant.
So, the correct option is B) a reflection of the line segment across y-axis.
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