Question

Find a so the distance between (x, 3) and (-7, 6) is √10x =__, __

Answer 1

Step-by-step explanation

The formula to find the distance between two points is:

`\begin{gathered} d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ \text{ Where }(x_1,y_1)\text{ and }(x_2,y_2)\text{ are the coordinates of the points.} \end{gathered}`

So, in this case, we have:

`\begin{gathered} (x_1,y_1)=(x,3) \\ (x_2,y_2)=(-7,6) \\ d=√((x_2-x_1)^2+(y_2-y_1)^2) \\ √(10)=√((-7-x)^2+(6-3)^2) \\ $$\text{ Square both sides of the equation}$$ \\ (√(10))^2=(√((-7-x)^2+(6-3)^2))^2 \\ 10=(-7-x)^2+(6-3)^2 \\ 10=(-7-x)^2+3^2 \\ 10=(-7-x)^2+9 \\ \text{ Subtract 9 from both sides} \\ 10-9=(-7-x)^2+9-9 \\ 1=(-7-x)^2 \\ $$\text{ Apply square root to both sides of the equation}$$ \\ √(1)=√((-7-x)^2) \\ 1=-7-x \\ \text{ Add 7 from both sides} \\ 1+7=-7-x+7 \\ 8=-x \\ \text{ Multiply by -1 from both sides} \\ 8*-1=-x*-1 \\ -8=x \end{gathered}`

Therefore, the value of x that satisfies the given conditions is -8.

Answer
`x=-8`