Question

What is the distance for A(6,0), B (-4,5)

Answer 1

Answer:

$5\sqrt{5}$

Step-by-step explanation:

The distance formula states that $D(x_{1} ,y_{1})(x_{2},y_{2} )=\sqrt{(x_{2} } -x_{1} )^2+(y_{2}-y_{1} )^2$

We plug in our points, (6,0) and (-4,5), and compute.

$\sqrt{(-4-6)^2+(5-0)^2} \\\sqrt{(-10)^2+5^2} \\\sqrt{100+25} \\\sqrt{125} \\5\sqrt{5}$ (Make sure you see why I put parentheses around the -10 in (-10)^2. -x^2 and (-x)^2 are not the same) (Also here is why the simplification of the radical works)

$\sqrt{125} =\sqrt{5^2*5} =\sqrt{5^2} *\sqrt{5} =5*\sqrt{5} =5\sqrt{5}$

The * stands for multiplication.