Math Help Please I don't know if I'm doing this right?

Question

Find the distance between (– 3, – 2) and (1, 4).

1 – ( -3 )^2 + 4 – ( -2 )^2
4^2 + 6^2
16 + 36
52

52 = 13 * 4

52 = 26 * 2
26 = 13 * 2

I'm pretty sure I'm doing this right but the examples in my text are not giving a similar answer to go off of. Is there any other multiples of 52 besides 13 * 4 and 26 * 2. Can someone please help.........

Answer 1

d = sqrt[(4-(-2))^2 + (1-(-3))^2]
d = sqrt(6^2 + 4^2)
d = sqrt(36 + 16)
d = sqrt(52)
d = sqrt(4*13)
d = sqrt(4)*sqrt(13)
d = 2*sqrt(13) <------exact answer
d = 7.2111 <------approximate answer

Answer 2

Find the distance between (– 3, – 2) and (1, 4)

Use Pythagorean theorem: x^2 + y^2 = r^2

x distance = 1 - (-3) = 4
y distance = 4 - (-2) = 6

x^2 + y^2 = 4^2 + 6^2 = 16 + 36 = 52

r = sqrt(52) = ~7.21

Answer 3

Your answer is not correct.
You are missing the square root over the entire formula.

2 points are (x1,y1) and (x2,y2)

The distance between 2 points is:
sqrt((x2 - x1)^2 + (y2- y1)^2)

in your case,
x1 = -3 y1 = -2
x2 = 1 y2 = 4
so:
sqrt ((1-(-3)^2 + (4-(-2)^2)
sqrt (( 4^2 + 6^2 )
sqrt( 16 + 36 )
sqrt (52) or sqrt (4*13) which is 2 * sqrt (13)

The distance between the 2 points is 2 times the square root of 13.

Answer 4

Ok, this is the formula. All of this is under one big square root sign.(X-X)^2+(Y-Y)^2.

So -3-1=-4^2 is 16.
And -2-4=-6^2 is 36.
16+36=52.
Find the prime factorization to simplify radical 52.
So, the answer is 2 radical 13.

Answer 5

Distance formula

d = √(x₂- x₁0 + (y₂- y₁)

d = √[1 - (- 3)²] + [4 - (- 2)²]

d = √(1 + 3)² + (4 + 2)²

d = √(4)² + (6)²

d = √16 + 36

d = √52

d = 7.211102551

- - - - - - - - -s-

Answer 6

52 X1