Dimensions of a rectangle from coordinates

rectangle ABCD is graphed in the coordinate plane the following are the vertices of the rectangle and they give us the labels for the vertices as well given these coordinates what is the length of side ad of this rectangle so let's just plot it that's one way that we could tackle it so let's let me see all of these are actually in the first coordinate so I can focus on the first coordinate so let's say that's my y-axis it's my y-axis and let me draw my x-axis my x-axis and actually I want to really focus in on the points a and D because we just need to find the length of the side from point A to point D so point a let me just in another color so point a is at x equals 7 y is equal to 1 so 1 2 3 4 5 6 7 so that's x equals 7 y is equal to 1 Y is equal to 1 so that is point a right over there point a let me label it point a and then where is point D point D has the exact same has the exact same x coordinate but its y-coordinate is a little bit higher its y-coordinate is 6 it's actually 5 higher so Point D is at x equals 7 Y is equal to 6 so Y is equal to 1 2 3 4 5 and 6 so that's y is equal to 6 and so we can draw the point it is going to be right over here this is point D and we can actually connect them with a line if we like to show that this is a side of a rectangle so let me draw that I can just draw this like this and there you have it I haven't even drawn the whole rectangle yet but just by plotting these two points we can think about how long side a D is we can say look the X doesn't change going from A to D but we do increase in the y-direction by 5 we go from Y is equal to 1 to Y is equal to 5/2 Y is equal to 6 so our change in Y is equal to 5 so what's the length of this line it's going to be five it's going to be five whatever the units are so that's the length of side ad it's going to be equal to five we went from the point seven comma one to the point to the point seven comma six now they said that this was a rectangle not just for satisfaction we can draw the entire rectangle we have the point B that is that x equals 5 y is equal to one so let me draw that and I'm just doing this just for fun now at this point we're done with a problem so x equals 5 y equals 1 that's right over here that's point B let me write B that's the point 5 comma 1 and then we have the Point C I'll do this in another color the Point C is that x equals 5 y equals 6 x equals 5 y equals 6 Point C is right over here Point C is the point x equals 5 y is equals 6 and then we can connect all the dots if we like and clearly see that it is a rectangle so I could connect those I could connect these two and I could connect these two and then we see that we indeed have a rectangle but we answered it a while ago that the length of side a D is equal to 5 if we cared about the other sides the length of B a well this is 2 we just we a difference of 2 along the x-direction the horizontal Direction just difference of 2 along the X Direction difference of 5 in the Y direction we go from y equals 1 to y equals 6 so there you have it we are actually able to figure out all of the dimensions of this rectangle