Parallelogram on the coordinate plane

you are graphing polygon ABCD in the coordinate plane the length of segment a B must be the same as the length of segment DC and both segments are horizontal segments the following are three of the vertices of the polygon so vertex a is at the point 1 comma 1 so 1 comma 1 it puts us right over there that is vertex a vertex C is at the point 4 point 5 comma 4 so 4 point 5 along the horizontal axis comma 4 comma 4 so we go all the way we go all the way up to all the way up to 4 so that right over there is Point C Point D is that negative 1 point 5 comma 4 so negative 1 point 5 along the horizontal or I guess you know the x-axis we could say negative 1 point 5 comma 4 so 4 along the vertical or the y-axis so go right up go right over there that's close enough so that of course is our y-axis this is point D and we need to figure out where what are the coordinates of point B if B must be in quadrant one and they tell us that the distance from A to B must be the same as the length of segment D to C and both are horizontal so let's draw what we know to draw so DC segment DC segment DC is this segment right over here is this segment right over here and we see it's horizontal both of the vertical coordinates are 4 at both vertex D and vertex C so both of the vertical coordinates are 4 now what is the length of this because we're going to construct another segment that has the same length well along the horizontal direction we went from negative 1 point 5 to 4 point 5 so how far did we go well to go from negative 1 point 5 to 0 you go 1 point 5 and then you have to go another 4 point 5 so this is going to be 4 point 5 plus 1 five which is equal to four plus one is five point five plus zero point five is 1 so 5 plus 1 is 6 so this distance right over here is 6 of our units another way of thinking about it and actually let me put the coordinates in here just so it becomes a little bit clearer this was the point four point do they need something easier to see this right over here is a point four point 5 comma 4 and this right over here is the point is the point negative 1 point 5 comma 4 and so another way of thinking about this distance is you could take the end point and we really to think about the distance just along its a horizontal line so the Y value does not change it doesn't change in the vertical direction only the horizontal so you really want to say well how far is Nate if you start at negative one point five and you get to four point five how far have you gone so you can just take your end point your end value your end horizontal value and X value and from that you can subtract your starting x-value so you subtract negative one point five and this of course is equal to four point five plus positive one point five which once again is equal to is equal to 6 so fair enough and let me draw some of the rest of the polygon just so we see it is indeed a polygon so we have this side right over here and it looks like it's going to be a parallelogram so we have this side right over here and we have to replace point B and point B is going to be someplace out here it has to be it's going to have the same vertical value or the same y values point a so it's y-coordinate is going to be 1 so point B is going to be out here someplace point me just in a new color so point point B and use this orange yet actually I have you see orange yet I haven't used the yellow now I've used the yellow C I haven't used this green point B is going to be someplace out here so point B is going to be someplace out here we already know what its y-coordinate is it's a horizontal line so it's going to have to have the same exact y-coordinate as point a point a is y-coordinate was 1 so this is going to have to a y-coordinate of 1 now the big question is what is what is its x-coordinate going to be well it's going to have to be in a different color it's going to have to be whatever a x-coordinate was it's going to have to be whatever a x-coordinate was and we see that a is x-coordinate was 1 it's going to have to be that plus 6 because we're going to move the same distance in the horizontal direction this thing has to be 6 so if we start at 1 we add 6 we get to 7 so what are the coordinates of point B and if specially if point B must be in quadrant one and notice we are definitely in quadrant one this is quadrant one this is quadrant two this is quadrant three and this is quadrant four coordinate for point B is 7 comma one