question to solve this math problem?

Question

I have vertex A=(0,-5) and B=(-3,-1)
Using the distance formula , i have to find the length of the side..

I solved the equation and got SQRT 13, is this right or am I wrong?? Another source tells me is SQRT 65. If I am wrong, please show me how to solve it . If Im right please let me know. Thanks.

Answer 1

I get 5:

The difference in the y coordinates is:
-5 - (-1)
= -5 + 1
= -4
But for a length we take the absolute value --> 4

The difference in the x coordinates is:
0 - (-3)
= 0 + 3
= 3

So you have two sides of 3 and 4. The hypotenuse can be found by remembering the special 3-4-5 triangle, or using the Pythagorean theorem.

a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²
c = sqrt(25)
c = 5

In general, the distance is sqrt((Δx)² + (Δy)²) where Δx is the change in x coordinates and Δy is the change in y coordinates. I think you made a mistake and accidentally got sides of 3 and 2, rather than 3 and 4.

Answer 2

The distance equation is sqrt((x2-x1)^2 + (y2-y1)^2)

= sqrt( ( -3 - 0 )^2 + ( -1 - (-5) )^2 )
= sqrt( ( -3 )^2 + ( -1 + 5 )^2 )
= sqrt( 9 + 4^2 )
= sqrt( 9 + 16 )
= sqrt( 25 )
= 5

Answer 3

The horizontal distance is -3-0 = -3 and
the vertical distance is -1-(-5)= 4 and it looks like you've
got the good ol' 3:4:5 right triangle. Any carpenter could
have told you that. Length is 5.
Pythag says ((-3)^2 + 4^2)^1/2 = (9+16)^1/2=25^1/2 =5

Answer 4

distance = sqrt[y1 - y2)^2 + (x1 - x2)^2]
= sqrt[(-5 - (- 1))^2 + (0 - (- 3))^2]
= sqrt[(-4)^2 + (3)^2]
= sqrt[16 + 9]
= sqrt[25]
= 5

Answer 5

distance between two cartesian points:

dist = sqrt(deltaX^2 + deltaY^2)

deltax = change in x co-ords = -3 - 0 = -3
delay = change in y co-ords = -1 - (-5) = 4

SO dist = sqrt( (-3)^2 + 4^2 ) = sqrt( 9 + 16) = 5

Answer 6

2x + 2y = 20 employing the simultaneous approach 2x - 2y = 4 ____________ 4x = 24 ( divide via 4) x = 6 replace x in one in all the two equations 2x + 2y = 20 2 (6) + 2y = 20 12 +2y = 20 2y = 20 - 12 2y = 8 (divide via 2) y = 4 answer : X = 6 , Y = 4