Performing reflections: rectangle (old)

Perform a reflection over the line y is equal to negative 1/3 x. And then they want us to figure out what these different points map to on the reflection. And then they ask, is the slope of the segment between point A and its image is, and then blank, the slope of the segment between point B and its image. So let's just think about this step by step. So first, let's perform the reflection over the line y is equal to negative 1/3 x. So we want to reflect. So negative 1/3 x. So its y-intercept is 0. And it has a slope of negative 1/3, which means every time-- whoops, so let me put this right over here-- and that means every time we move positive 3 in the x direction, we move down once in the y direction. So this right over here, this is y is equal to negative 1/3 x. And so let's do our reflection. Whoops. To do the reflection, I've got to press this. So let's do our reflection. There we go. All right, this is exciting. So what does point A map to? Well, point A maps to this point right over there. And so that is the point negative 4, 8. And point B maps to this point, which is the point 8, positive 4. And then, they say the slope of the segment between point A and its image, so that's this segment between point A and its image. So actually let me take this reflection tool to just show you that line. So that's this segment right over here. The slope of the segment between point A and its image, that's this slope right over here, is blank the slope of the segment between point B and its image. Well, point B and its image, that line right over here, is going to have the same slope. And that makes sense, because they're both going to be perpendicular to what we were reflecting around. They're both going to be perpendicular to y is equal to negative 1/3 x. So they're going to have a negative reciprocal of negative 1/3 slope, which is positive 3. And you see this has a slope of positive 3, and that this right over here has a slope of positive 3. Every time you increase one in the x direction, you increase y by three units. So the slope is equal to. And we check our answer. And we got it right.