Question

Write the ordered pair that represents yz. Then find the magnitude of yz
Y(3,1), Z(0,4)

Answer 1

(-3, 3),
`2√(2)`

Explanation:

I'm assuming this is a vector problem. See the graph for the vector from Y to Z (the tail is at point Y, the head is at point Z).

This vector is equivalent to one which is the same length and in the same direction with its tail at the origin. That vector's head is at (-3, 3) -- the blue one.

To get that, subtract the tail of the original vector from the head of the original vector.

(0, 4) - (3, 1) = (0 - 3, 4 - 1) = (-3, 3)

The magnitude of the blue vector is its length. Use the Distance Formula.

`√((x_2 - x_1)^2+(y_2-y_1)^2) \\ √((-3-0)^2+(3-0)^2) \\ √(9+9) \\ √(18)`

This simplifies to
`3√(2)`