Geometry Homework

Question

Very Important !

Triangle ABC has vertices A(1,2), B(4,6), C(4,2). The triangle will be reflected over the x-axis and then rotated 180 degrees about the origin to form Triangle A”B”C”. What are the new vertices of B?

A. (4,-6)

B. (-4,-6)

C. (4,6)

D. (-4,6)

Answer 1

Hi Leah

When a point is reflected over the x-axis, then its y-coordinate becomes the opposite of where it started.

In mapping notation, (x,y)→(x,-y)

That means that after the reflection, B(4,6)→B'(4,-6)

When a point is rotated 180 about the origin, then its x and y coordinates both become opposite.

In mapping notation, (x,y)→(-x,-y)

That means that after the rotation, B'(4,-6)→B''(-4,6)

It looks like you're working your way through all the isometries, so let me also add that rotating a point 90° counter-clockwise about the origin is mapped as (x,y)→(-y,x), rotating a point 90° clockwise about the origin is mapped as (x,y)→(y,-x), and translating a point by a vector <a,b> is mapped as (x,y)→(x+a,y+b)

Let me know if you have any questions about any of this!