find the values of y if the distance between the two points (10,y) and (16,2) is 10.
i wrote down the distance formula:
10=SQRT(16-10)squared + (2-y)squared
now how do i solve for y??
10 = sqrt (6^2+(2-y)^2)
square both sides
100 = 36 +4 -4y +y^2
60 = y^2 - 4y
y^2 - 4y - 60 = 0
(y-10)(y+6) = 0
y = 10 or - 6
if y = 10
d^2 = 36+ 64
d^2 = 100 yes, works
if y = -6
d^2 = 36 + 64 yes
so either 10 or - 6 work
thnks alot
To solve for y, you can follow these steps:
1. Start with the distance formula:
10 = √((16 - 10)^2 + (2 - y)^2)
2. Square both sides of the equation to eliminate the square root:
100 = (16 - 10)^2 + (2 - y)^2
3. Simplify the equation:
100 = (6)^2 + (2 - y)^2
100 = 36 + (2 - y)^2
4. Subtract 36 from both sides:
100 - 36 = (2 - y)^2
Simplify:
64 = (2 - y)^2
5. Take the square root of both sides:
√64 = √((2 - y)^2)
Simplify:
8 = 2 - y
6. Now, isolate y by subtracting 2 from both sides:
8 - 2 = -y
Simplify:
6 = -y
7. Finally, multiply both sides by -1 to solve for y:
-6 = y
Therefore, the value of y is -6.