Math Help Please?

Question

Please answer these two questions I am having trouble solving them in my geometry class their the only problems I don't understand.

Find the distance between the two points

(0,0) (5,2)
(3,0) (8,10)

Thanks

Answer 1

Use the distance formula:
d = sqrt of ( (x2 - x1)^2 + (y2 - y1)^2 )

d = sqrt of ( 5^2 + 2^2 )
d = sqrt of (25 + 4)
d = sqrt of 29

d = sqrt of (5^2 + 10^2)
d = sqrt of 125
d = sqrt of (25 * 5)
d = 5 * sqrt of 5

Answer 2

First, you're going to use the pythagorean theorem, which is that a^2 + b^2 = c^2 for a right triangle.

Now the line from (0,0) to (5, 2) goes up by 2 and over by 5, so the square of the length of the line is 5^2 + 2^2 = 25 + 4 = 29 . The length is the square root of 29 .

The line from (3,0) to (8,10) goes over by 8-3 = 5 and up by 10 - 0 = 10 . The sqaure of the length of the line is 10^2 + 5^2 = 100 + 25 = 125 . The length is the square root of 125 = 5 times the square root of 5.

Answer 3

This uses pythagoras. To calculate the distance, work out the distance in terms of horizontal and vertical parts then, as it is a right angled triangle, use pythagoras to calculate the hypoteneuse (i.e. the direct line between the two points).

As an example, the second solution is as follows.

Calculate the horizontal distance (change in x)
8 - 3 = 5

Calculate the vertical distance (change in y)
10 - 0 = 10

Now, using pythagoras, h² = a² + b²
h² = 5² + 10²
h² = 25 + 100
h² = 125
h = √125
h ≈ 11.2

The distance between the two points is approx 11.2 units

Answer 4

distance between two pts; (x1,y1) & (x2,y2)
= sqrt ( (x2-x1)^2 + (y2 - y1)^2)

between (0,0), (5,2)
dist = sqrt ( 2^2 + 5^2 )
sqrt( 4 +25) = sqrt(29)
= 5.385

between (3,0), (8,10)
dist = sqrt ( (8-3)^2 + (10-0)^2 )
= sqrt ( 25 + 100 )
= sqrt(125)
= 11.18

Answer 5

i'm maths instructor sending you this guidance: a million) do no longer restoration special time, 2) interest is the motivating element to assessment arithmetic. 3) very maximum intense element to be stated is "practice Examples and workouts in effortless terms. 4) do no longer bypass over any financial ruin. 5) while you're a pupil of state board,do no longer study something from out area the text fabric e book. 6) Refer previous 365 days questions. 6) if ISC, you ought to refer extra books. 7) interest and problematic artwork with effective could carry you 100p.c.successes

Answer 6

(0,0) (5,2)
root of { (5-0)^2 + (2-0)^2 } = root of 29

(3,0) (8,10)
root of { (8-3)^2 + (10-0)^2 } = root of 125

Answer 7

change in y over change in x = slope
2-0=2
5-0=5 so 2/5

10-0=10
8-3=5 so 10/5 or 2

Answer 8

distance formula: the square root of ((x2 - x1)squared + (y2 - y1)squared)
or the square root of ((5 - 0)squared + (2 - 0)squared)
= the square root of ((5)squared + (2)squared)
= the square root of (25 + 4)
= the square root of 29

The other one is just the same, but you do (8 - 3) and (10 - 0)

Answer 9

No answers from me, just a method: Think Pythagorean Theorem with the differences of the x's and y's as a and b.

Answer 10

distance between (x1,y1) and (x2,y2) is

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

So... sqrt((5-0)^2 + (2-0)^2)) = sqrt(29)

And sqrt((8-3)^2 + (10-0)^2)) = sqrt(125) = 5 * sqrt(5)