The distance between points A and B is 10 units. If a has coordinates (4,-6) and B has coordinates (-2,y), determine the value of y.
Please show work and explain.
A.-6
B.-2
C.0
D.1
E.2
This is what I got so far:
10= square root of (4-(-2))^2+(-6-(y))^2
(y+6)^2 + (-6)^2 = 100
y^2 + 12 y + 36 + 36 = 100
y^2 + 12 y - 28 = 0
(y-2)(y+14) = 0
y = 2 or -14
y = 2 is on your list
To determine the value of y, we need to use the distance formula. The distance formula calculates the distance between two points in a coordinate plane.
The formula is as follows:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, we have the coordinates of point A as (4, -6) and the x-coordinate of point B as -2. We need to find the y-coordinate of point B.
Let's substitute the given values into the distance formula:
10 = √((4 - (-2))^2 + (-6 - y)^2)
Now, let's simplify the equation:
10 = √((4 + 2)^2 + (-6 - y)^2)
10 = √(6^2 + (-6 - y)^2)
10 = √(36 + (-6 - y)^2)
We can square both sides of the equation to remove the square root:
10^2 = (36 + (-6 - y)^2)
100 = 36 + (-6 - y)^2
Next, we can simplify the equation further:
100 - 36 = (-6 - y)^2
64 = (-6 - y)^2
To eliminate the square on the right side of the equation, we can take the square root of both sides:
±√64 = ±(-6 - y)
Taking the positive square root:
√64 = -6 - y
8 = -6 - y
To solve for y, we can isolate it by moving the -6 to the other side of the equation:
8 + 6 = -y
14 = -y
y = -14
Therefore, the value of y is -14.
Based on the options provided, none of the given options match the value of y obtained (-14), so none of the choices listed are correct.