Question

a man has a sugearcane with end points A(3,2) and B(7,5) .
1.what will be the length of the sugarcane.
2.now he wants to distribute sugarcane AB for his children equally. then at what point will he cut the sugarcane equally​

Answer 1

1.

Here we will use distance formula:

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

Given points are A(3,2) and B(7,5)

So, the length of sugarcane:

$\boxed{\sqrt{(7-3)^2+(5-2)^2}} \\\\\sf =\sqrt{4^2+3^2} \\\\\sf = \sqrt{16+9}= \sqrt{25}= 5$

Hence, the length of sugarcane is 5 units

2.

To distribute sugarcane among how many children??

For 2 children, use midpoint formula, that is :

$[ \frac{(x_1+x_2)}{2},~\frac{(y_1+y_2)}{2}]$

Answer 2

Given: A man has a sugar cane with endpoints A(3,2) and B(7,5).

To find: 1- Length of sugarcane

2- The point the sugarcane should be cut to divide it equally among children

Explanation: A(3,2) and B(7,5)

Let x1=3, y1=2, x2= 7 , y2=5

The length is given by:

$\sqrt{ ({x2 - x1})^{2} + ( {y2 - y1)}^{2} }$

Putting values:

=$\sqrt{ {(7 - 3)}^{2} +{(5 - 2)}^{2} }$

=$\sqrt{ {(4)}^{2} + {(3)}^{2} }$

=5 units

For equal distribution point that should be cut is given by: (x1+x2/2, y1+y2/2)

Putting values:

Point= (3+7/2, 5+2/2)

= (5, 3.5)

Therefore, the length of the sugarcane is 5 units and the point at which sugarcane should be cut to divide equally is (5,3.5).