It is a given that △ ABC is similar to △ AYZ. We are asked to determine the coordinates of Z. Let's take a look at the following diagram where we have shown them overlapping on certain sides.
We will start with determining the side lengths of both triangles. To do this, we will use the Distance Formula. Let's start with the length of AB and substitute ( 0, 0) and ( ,4) into this formula.
Here is some great news, we can evaluate the rest of the side lengths in the same way as we just did with AB. Let's present those calculations in a table as follows.
Side
Points
Distance Formula
Side Length
AB
( 0, 0) & ( ,4)
sqrt(( - 0)^2+(4- 0)^2)
4
AY
( 0, 0) & ( ,8)
sqrt(( - 0)^2+(8- 0)^2)
8
AC
( 0, 0) & (6, )
sqrt((6- 0)^2+( - 0)^2)
6
Now, let's recall that in similar triangles corresponding sides are proportional. Using this information, we will create a proportion.
AB/AY=AC/AZ
Next, we will substitute appropriate side lengths into this proportion and solve for AZ.
