How do you find the distance between between two points without graphing?

Question

For example, if you are only given these points:

a) (0, 5) and (5, 0)

b) (-4, 7) and (29, 76)

Answer 1

You use the pythagorean theorem. a^2 + b^2 = c^2.

You subtract the first x value from the second x value and square it. Subtract the first y value from the second y value, and square it. Add both togethor and take the square root. This is the distance between the two points.

x1=0, x2=5
y1=5, y2=0

(5-0)^2+(0-5)^2 = 25 + 25 = 50
square root(50) = 5 square root(2)

Answer 2

Use the pythagorean theorem. The line will be the hupotenuse of a right triangle with Δx & Δy being the legs
a) z^2=(0-5)^2+(5-0)^2
z^2=25+25=50
z=5√2=7.07

b) z^2=(-4-29)^2+(7-76)^2
z^2=33^2+69^2
z^2=1089+4761
z^2=5850
z=76.485

Answer 3

[a]
delta y = 5
delta x = 5
then apply a^2 + b^2 = c^2
5^2 + 5^2 = c^2
25 + 25 = c^2
50 = c^2
c (distance) = sqrt(50) = 7.???

[b]
delta x = 29 - (-4) = 33
delta y = 76 - 7 = 69
33^2 + 69^2 = c^2
calculate same way as above

Answer 4

Set at any element of a line.- That formulation is for the area from a element to a on the instant line .- enable x=0 , y= a million/5 ( firs line, f occasion) D= (3(0) +5(a million/5) +9)/ sqrt( 9+25) ( 2d line) D= 10/sqrt34 .-

Answer 5

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

d = sqrt[ (5 - 0)^2 + (0 - 5)^2 ]
d = sqrt[ 50] = 5* sqrt(2)

d = sqrt[ (29 - -4)^2 + (76 - 7)^2 ]
d = sqrt[ (33)^2 + (69)^2 ]
d = sqrt[ 5850 ]
d = sqrt[ 225 * 26 ]
d = 15sqrt[ 26 ]

Answer 6

use the distance formula: D=sqrt((x_2-x_1)^2+(y_2-y_1)^2). Here, the points given are (x_1,y_1) and (x_2,y_2). In the case of part (a),

x_1=0
x_2=5
y_1=5
y_2=0

so we have D=sqrt((5-0)^2+(0-5)^2) = sqrt(25+25) = sqrt(50) = 5sqrt(2).

In the case of part (b),

x_1=-4
x_2=29
y_1=7
y_2=76

so D=sqrt((29 - (-4))^2 + (76-7)^2) = sqrt( 1089 + 4761) = sqrt(5850) = 3sqrt(650) = 76.485...

Answer 7

Distance between points P(x1,y1) and
P2(x2,y2) is given by d where:
d² = (x2- x1)² + (y2 - y1)²
d = √ [ (x2 - x1)² + (y2 - y1)² ]

Answer 8

distance formula
D=sqrt((x2-x1)^2+(y2-y1)^2)