Question

1) in a plane on coordinate axes, coordinate of points A,O and B are (4,0), (0,0) and (-3.0) respectively. find the distance AB
pls answer fast....

2)divide 12* 4 root15 by 8*3 root 3

Answer 1

DIstance between two points A(x1, y1) and B(x2, y2) is equal to

   $\sqrt{(x2 - x1)^2 + (y2 - y1)^2} \\ \\ \sqrt{(-3 - 4)^2 + (0-0)^2} \\ \\ \sqrt{(-7)^2} \\ \\ \sqrt{49} = 7$

LOOK at the diagram for better understanding

2)  

$\frac{12 * 4 * \sqrt{15}}{8 * 3 \sqrt{3}} \\ \\ \frac{12 * 4 * \sqrt{5*3}}{8 * \sqrt{3}} \\ \\ \frac{6 * 2 * 4 * \sqrt{5} * \sqrt{3}}{2 * 4 * \sqrt{3}} \\ \\ 6 * \sqrt{5}$

Answer 2

i) 
The distance between two points $(x_1, y_1) and (x_2, y_2)$ is

$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }$

A( (4,0) and B(-3,0)

AB = $\sqrt{(-3-4)^2 + (0-0)^2 }$

$= \sqrt{(-7)^2 }$

AB = 7

ii) divide 12* 4 root15 by 8*3 root 3

$\frac{12*4 \sqrt{15} }{8*3 \sqrt{3} }$

$\frac{48 \sqrt{15} }{24 \sqrt{3} }$

$\frac{2\sqrt{3}\sqrt{5} }{\sqrt{3} }$

$2 \sqrt{5}$