The distance, d, between two points, (x1,y1) and (x2,y2), can be found using the formula d=√(x2−x1)^2+(y2−y1)^2
How can you rearrange the given formula to correctly find y2?
the distance between the points x ,y and x,y two is give by
To find "y2" in the given formula, we need to rearrange it. Let's start by isolating the term "(y2 - y1)^2" on one side of the equation.
1. Start with the original formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
2. Square both sides of the equation to remove the square root: d^2 = (x2 - x1)^2 + (y2 - y1)^2
3. Expand the right side of the equation: d^2 = (x2 - x1)(x2 - x1) + (y2 - y1)(y2 - y1)
4. Multiply out the terms: d^2 = (x2^2 - 2x1x2 + x1^2) + (y2^2 - 2y1y2 + y1^2)
5. Rearrange the equation to isolate the y2 term: d^2 - x2^2 + 2x1x2 - x1^2 - y1^2 = y2^2 - 2y1y2
6. Simplify the equation further: y2^2 - 2y1y2 = d^2 - x2^2 + 2x1x2 - x1^2 - y1^2
7. Factor out y2 on the left side of the equation: y2(y2 - 2y1) = d^2 - x2^2 + 2x1x2 - x1^2 - y1^2
8. Divide both sides of the equation by (y2 - 2y1): y2 = (d^2 - x2^2 + 2x1x2 - x1^2 - y1^2)/(y2 - 2y1)
Therefore, the rearranged formula to find y2 is:
y2 = (d^2 - x2^2 + 2x1x2 - x1^2 - y1^2)/(y2 - 2y1)
To rearrange the formula to find y2, we need to isolate it on one side of the equation.
Starting with the given formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
To begin, let's square both sides of the equation to eliminate the square root:
d^2 = (x2 - x1)^2 + (y2 - y1)^2
Next, move (x2 - x1)^2 to the right side by subtracting it from both sides:
d^2 - (x2 - x1)^2 = (y2 - y1)^2
Now, we can take the square root of both sides to isolate (y2 - y1):
√(d^2 - (x2 - x1)^2) = y2 - y1
Lastly, add y1 to both sides to solve for y2:
y2 = √(d^2 - (x2 - x1)^2) + y1
So, the rearranged formula to find y2 is:
y2 = √(d^2 - (x2 - x1)^2) + y1.
square both sides of d=√(x2−x1)^2+(y2−y1)^2
d^2 = x2^2 - 2(x2)(x1) + x1^2 + y2^2 - 2(y2)(y1) + y1^2
d^2 - x2^2 + 2(x2)(x1) - x1^2 - y1^2 = y2^2 - 2(y2)(y1)
y2^2 - 2(y2)(y1) - d^2 + x2^2 - 2(x2)(x1) + x1^2 - y1^2 = 0
compare with the standard quadratic, we have
a = 1
b = -2y1
c = - d^2 + x2^2 - 2(x2)(x1) + x1^2 - y1^2
Now solve for y2 using the quadratic equation, rather unruly mess