(02.02 MC) Triangle ABC is shown. A is at negative 2, 1. B is at negative 1, 4. C is at negative 4, 5. If triangle ABC is reflected over the x‐axis, reflected over the y‐axis, and rotated 180 degrees, where will point B' lie? (−1, 4) (1, −4) (4, −1) (−4, 1)

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Avaburdisgo Avaburdisgo · Answer 1

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].

Erinnago Erinnago · Answer 2

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.

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