It is a given that △ ABC is similar to △ AYZ. We are asked to determine what the coordinates of B are.
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 AY and substitute ( 0, 0) and ( ,-6) into this formula.
We will determine the values of the other side lengths in the same way as we found AY. Let's express these sides, their coordinates, the substitution of their coordinates into the Distance Formula, and their side length by using a neatly organized table.
Side
Points
Distance Formula
Side Length
AY
( 0, 0) & ( ,-6)
sqrt(( - 0)^2+(-6- 0)^2)
6
AC
( 0, 0) & (4, )
sqrt((4- 0)^2+( - 0)^2)
4
AZ
( 0, 0) & (12, )
sqrt((12- 0)^2+( - 0)^2)
12
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 AB.
