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Sagot :
Answer:
(-1,4)
Step-by-step explanation:
Point B in the pre-image is at (-1,4).
If triangle ABC is reflected over the x‐axis, the y-coordinate changes to its negative value, thus we have the transformation:
Next, if the point (-1,-4) is reflected over the y‐axis, the x-coordinate changes to its negative, Thus, we have the transformation:
Finally, a rotation by 180 degrees will give the coordinates of B' as:
The point B' will lie in (-1, 4) [ the same place as B].
The coordinates of point B' are [tex](-1,4)[/tex]. So, the first option is correct.
Given:
The vertices of a triangle ABC are [tex]A(-2,1), B(-1,4)[/tex] and [tex]C(-4,5)[/tex].
Triangle ABC is reflected over the x‐axis, reflected over the y‐axis, and rotated 180 degrees.
To find:
The point B'.
Solution:
If a figure reflected over x-axis, then
[tex](x,y)\to (x,-y)[/tex]
[tex]B(-1,4)\to B_1(-1,-4)[/tex]
If a figure reflected over y-axis, then
[tex](x,y)\to (-x,y)[/tex]
[tex]B_1(-1,-4)\to B_2(-(-1),-4)[/tex]
[tex]B_1(-1,-4)\to B_2(1,-4)[/tex]
If a figure rotated 180 degrees about the origin, then
[tex](x,y)\to (-x,-y)[/tex]
[tex]B_2(1,-4)\to B'(-(1),-(-4))[/tex]
[tex]B_2(1,-4)\to B'(-1,4)[/tex]
So, the coordinates of point B' are [tex](-1,4)[/tex].
Therefore, the first option is correct.
Learn more:
https://brainly.com/question/12907061
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