Finding The Missing Coordinate of a Corner of a Kite or Isosceles Triangle.

To find the missing coordinate of a corner of a shape all you need to do is mark out the numbers on the x and y axis. Make sure you put the first number of each coordinate on the x axis and the second number of each coordinate on the y axis.

Let’s take a look at a couple of examples, both examples are fairly difficult as one example is a kite shape and the other an isosceles triangle.

Example 1

Work out the missing vertex of this isosceles triangle (a,b)

To begin with, mark the numbers on the x and y axis of the coordinate grid.

On the x axis put 2 and 6 as these are the first numbers of the coordinates.

On the y axis put 5 and 23 as these are the second numbers of the coordinates.

Now b is equal to 5, but a is going to be a little harder to work out.

Since the shape is isosceles and there is a line of symmetry down the centre of the kite, the difference between 2 and 6 will be the same as the difference between 6 and b. Now the difference between 2 and 6 is 4, so if you add 4 onto 6 this will give you 10.

So out missing coordinate is at (10,5).

Example 2

Work out the missing vertex of this kite (c,d).

As before, first mark the numbers on the x and y axis of the coordinate grid.

On the x axis put 13 and 18 as these are the first numbers of the coordinates.

On the y axis put 3, 42 and 44 as these are the second numbers of the coordinates.

Now it is obvious that d = 42, but like example 1, c is going to be a little harder to find.

Like the isosceles triangle in example 1, a kite has one line of symmetry down the centre of the shape. Therefore the difference between 13 and 18 will be equal to the difference between 13 and c. Since, the difference between 13 and 18 is 5, you can take 5 away from 13. So c = 8.

So out missing coordinate is at (8,42).

For some easier questions on shape problems involving rectangles click here.

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