Answer:
[tex]z = (6,-1)[/tex]
Step-by-step explanation:
The missing parameters are:
[tex]x = (3,-1)[/tex]
[tex]y = (3,5)[/tex]
[tex]yz= \sqrt{45[/tex] --- Hypotenuse
Required
The coordinate of Z
First, calculate the distance xy
[tex]xy = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]xy = \sqrt{(3 - 3)^2 + (-1 - 5)^2}[/tex]
[tex]xy = \sqrt{0 + 36}[/tex]
[tex]xy = \sqrt{36}[/tex]
[tex]xy = 6[/tex]
By Pythagoras theorem, distance xz is:
[tex]yz^2 = xz^2 + xy^2[/tex]
[tex](\sqrt 45)^2 = xz^2 + 6^2[/tex]
[tex]45 = xz^2 + 36[/tex]
Collect like terms
[tex]xz^2 =45-36[/tex]
[tex]xz^2 =9[/tex]
[tex]xz = \sqrt{9}[/tex]
[tex]xz = 3[/tex]
This means that z is 3 units to the right of x
We have:
[tex]x = (3,-1)[/tex]
The rule to determine z is:
[tex](x,y) \to (x + 3, y)[/tex]
So, we have:
[tex]z = (3 + 3,-1)[/tex]
[tex]z = (6,-1)[/tex]
