Mastering Coordinate Geometry: Finding Missing Coordinates in Rectangles (Full Transcript)

Speaker 1: I am Anil Kumar. Welcome to my series on coordinate geometry. Finding missing coordinates is always a very interesting question and is seen in many test papers. So I hope this example will help you to perform better in some test papers. The question here is ABCD is a rectangle, point A is 210, B is minus 1 6 and C lies on the x-axis. Find coordinates of point D. Let's try to sketch this and then we'll continue with this solution. So let's say that is x and y axis. We are given point A as 210, this is somewhere there, right, and point B is minus 1 6, let's say somewhere there, right, and then let's join them. Now this is a rectangle, so let me just draw a line parallel to this and complete the rectangle. Okay, this doesn't seem like, let's say this, okay. So we, it's a approximate diagram, definitely not to the scale, but that is how it looks. A is 210, okay, A is 210, B is minus 1 and 6, C is on the x-axis. So we could write this coordinate as, let us say x values A and y value will be 0. As far as D is concerned, we'll use point x and y. We need to find coordinates of point D. We also know this is a rectangle, so all these are at right angles and these are of course parallel, okay. Now how do we find these coordinates? Let's first figure out what is C. Now we know that AB is perpendicular to BC, right, so the line AB is perpendicular to BC and that really means that the slope of AB will be negative reciprocal slope of BC, correct. So slope of AB is, slope in general, M is y2 minus y1 over x2 minus x1. So slope of A to B could be 10 minus 6 divided by 2 minus minus 1, which is 2 plus 1, and negative MBC. Slope of B to C, difference in y values, 0 minus 6, that comes in the denominator this time, A minus minus 1 means A plus 1, okay, so we get this. So that is what we get and this ratio on the left side is 4 is to 3 equals to minus A plus 1 over minus 6, so that becomes positive, so we can just make this positive. We can find the value of A, just cross multiply, 6 times 4 over 3 equals to A plus 1, and this is, that goes two times, so A plus 1 is 8, so we get A equals to 8 minus 1, which is 7. So we get the coordinates of point C as as 7, 0, right, so this point basically is 7, 0. Now it is easier to find coordinates of point D. We can now equate these two slopes, right, so we know slope AB is equal to slope C to D, right. Slope A to B we just found is 4 over 3, we are using this value, 4 over 3, right, which we calculated, that should be equal to slope of C to D. Now that is y minus 0, that is y minus 0, divided by x minus 7. Now from here, y should be equal to 4, that means 4 is equal to y, we get one value, as far as x minus 7 is 3, we get 3 equals to x minus 7, or x equals to 3 plus 7, which is 10, right. So now we get the coordinates for point D, which are x value is 10, and the y value is 4, correct. So we get those two points also, so we get y equals to 4, and x equals to 10. So I hope you understand these steps involved to find this particular solution. So this is a very efficient way of finding the missing points. So what we did was that first we found C by equating perpendicular lines, and then we found C, D, by using parallel lines. Perfect? So I hope that makes sense. Feel free to write a comment, share your views, and if you like and subscribe to my videos, that'd be great. Thanks for watching, and all the best.