Find the distance between (0,2) and (5, -4).?

Answer 1

Look up the distance formula in your book!
You remember difference of x values squared plus difference of y values squared, all under a square root sign.
sqrt[(5-0)^2 + (-4-2)^2] = sqrt[(5)^2 + (-6)^2]
= sqrt[25 + 36]
And so on.
Note: Distance is always >= 0.

Answer 2

The distance between the x values is 5 - 0 or 5
The distance between the y values is 2 - -4 or 6

These are the legs of a right triangle. Use the Pythagorean Theorem. 5^2 + 6^2 = hypotenuse squared
25 + 36 = 61
hypotenuse = square root of 61 or 7.81

Answer 3

The distance between two points is given by the following formula:

d = sqrt ( (x2 - x1)^2 + (y2 - y1)^2 )

(Note the similarities between this formula and the slope formula. The difference between the x-values represents the distance between the x-points, and the difference between the y-values represent the distance between the y-points. If you plot these points and connect them, they form a right angle triangle, hence the secondary similarity with the Pythagoras theorem).

d = sqrt [ (5 - 0)^2 + (-4 - 2)^2 ]
d = sqrt [ 5^2 + (-6)^2 ]
d = sqrt (25 + 36)
d = sqrt (61)

Answer 4

difference in x is 5, different in y is 6.

for a triangle a squared + b squared = c squared

5^2 + 6^2 = 61

therefore the route of 61 is the distance = 7.81

Answer 5

Let the distance be d.

d^2 = (0-5)^2 + (2-(-4))^2
d^2 = 25 + 36
d^2 = 61
d = 61^(1/2)
d = 7.81025

Answer 6

It is -11.

Answer 7

Formula is sqrt of (X (2)- x (1))^2+ (Y(2)-Y(1))^2

it is equal to 7.81 units