Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

(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)

Sagot :

Avaburdis

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

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.