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perform a reflection over the line y is equal to negative one-third X and then they want us to figure out what these different points map to on the reflection and then they ask us 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 of 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 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 whoops they have to do the reflection I'm going to press this let's do our reflection there we go all right this is exciting so what is point a map to well point a maps to this point right over there and so that is the point negative 4 comma 8 negative 4 comma 8 and point B maps to this point which is the point 8 positive 4 8 positive 4 and then they say the slope of the segment between point a and its image so that's this 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 8 it's image that's this slope right over here is blank the slope of the segment between point B and it's image well point B in its image that line right over here it's going to have is going to have the same slope that's 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 gonna 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 three every time you increase one in the x-direction you increase y three by three units so the slope is equal to and we check our answer and we got it right