Question

How do you find the distance between the point A(6,3) and B(14,9)?

Answer 1

Distance `d_{AB}=10` units

Explanation:

Apply distance formula `d=\sqrt((y_2-y_1)^2+(x_2-x_1)^2)`

Given points `\color(red){(x_1,y_1)}\leftrightarrow(6,3)`, point A;
`\color(blue){(x_2,y_2)}\leftrightarrow(14,9)`, point B;
`d_(AB)=\sqrt{(\color(blue)(9)-\color(red)(3))^2+(\color(blue)(14)-\color(red)(6))^2}`
`\rArr\sqrt{(6)^2+(8)^2}\rArr\sqrt{36+64}\rArr\sqrt{100}\rArr10`

`d_(AB)=10` units