The answer is 4.60977222865 rounded to however much it asks you to round.
We are given:
x (-4, 3)
y (2, -1.5)
z (4, -1)
A (3, 3)
And we are trying to find the hypotenuse of triangle YZA because that’s what the line from “point A to XZ” is.
The Pythagorean Theorem is a^2 + b^2 = c^2
We can use it to find the distance between any two points. If we imagine 2 more lines, one going straight down from the higher point, and the other one going horizontally from the lower point until it meets the vertical line. We have another triangle.
The length of the horizontal segment of a triangle is just the difference of. the x values. And the length of the vertical segment is just the difference of their y values.
So we have
(x2 - x1)^2 + (y2 - y1)^2 = c^2
Simplified:
sqrt((x2 - x1)^2 + (y2 - y1)^2) = c
Segment YZ =
sqrt((x2 - x1)^2 + (y2 - y1)^2) = c
sqrt((4 - 2)^2 + (-1 - -1.5)^2) = c
sqrt(4 + .25) = c
sqrt(4.25) = c
2.06155281281 = c
The length of YZ is 2.06155281281.
Now we need to know segment ZA.
Segment ZA =
sqrt((x2 - x1)^2 + (y2 - y1)^2) = c
sqrt((3 - 4)^2 + (3 - -1)^2) = c
sqrt(1 + 16) = c
sqrt(17) = c
4.12310562562 = c
The length of segment ZA is 4.12310562562.
Finally:
AZ^2 = YZ^2 + ZA^2
AZ^2 = (2.06155281281)^2 + (4.12310562562)^2
AZ^2 = 4.25 + 17
AZ^2 = 21.25
AZ = sqrt(21.25)
AZ = 4.60977222865
