Question

(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)

Answer 1

Given:

The vertices of a triangle ABC are A(-2,1), B(-1,4) and C(-4,5).

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

$(x,y)\to (x,-y)$

$B(-1,4)\to B_1(-1,-4)$

If a figure reflected over y-axis, then

$(x,y)\to (-x,y)$

$B_1(-1,-4)\to B_2(-(-1),-4)$

$B_1(-1,-4)\to B_2(1,-4)$

If a figure rotated 180 degrees about the origin, then

$(x,y)\to (-x,-y)$

$B_2(1,-4)\to B'(-(1),-(-4))$

$B_2(1,-4)\to B'(-1,4)$

So, the coordinate of point B' are (-1,4).

Therefore, the correct option is A.