 So here's a couple of videos to get you introduced to the idea of coordinate proof now What coordinate proof is all about is it takes these shapes that we've been dealing with? Triangles and parallel lines and such and puts them on a series of coordinates in other words It puts them on an xy grid So to get us introduced to that here We have a triangle and we've got some missing coordinates and in a particular up top here. We've got the Point C has its x-coordinate is missing But there's enough information with the other coordinates so that we can find out what that coordinate is So take a look down here at point B Point B says its x-coordinate is 2p units in other words this distance is 2p units so there's One p and then another p units Now that's enough information given the fact that this is an isosceles triangle That's enough information for us to determine that the x-coordinate of point C is Also p units. Well, I guess that p is stuck there. So this distance is also p and So therefore this missing coordinate is Also p and then I guess it's q units tall So the difference with coordinate proof is We're not using numbers on an x-y grid. We're using variables and those variables could represent any possible numbers Let's try another example So here we have an isosceles triangle. I know it's isosceles because of these congruence marks It's also an isosceles right triangle as shown by this right angle symbol in the corner And our job is to find the x and y coordinates of of point T So in order to find point T we'll use the x-coordinate of S And that tells me that the x-coordinate from the origin this distance is 2a units And now if that distance is 2a Because we've got a right angle right angles are perpendicular That means this distance up top is also 2a And so the coordinates for T. Whoops Coordinates for T. We know it's x-coordinate is 2a as well And now we need to find the y-coordinate So that y-coordinate is related to the fact that this is an isosceles triangle Those green congruence marks show me that well if this distance is 2a then this distance must also be 2a And that length of course is the y axis so we have a height here of 2a as well And so the missing coordinates are 2a and 2a Let's take a look at one more example with positioning or finding the missing coordinates All right, so here we have another isosceles triangle We can tell it's isosceles from the fact that we've got the congruence marks here And the distance from the origin to g I know that distance is 2g units The reason it's 2g units is that's its x-coordinate And so if that distance oh that looks like an a it's supposed to be a g If that's 2g then this distance must also be 2g units However, it's 2g units in the negative x direction And so the x-coordinate of e would be negative 2g Since both point g and point e lie on the x-axis that tells me that the y-coordinate would be zero So e is at negative 2g and zero Now to find the x-coordinate for f I see that that point lies on the y-coordinate in other words It's x value its x-coordinate must be zero And so the coordinates for point f would be zero b