Question

The coordinate of the point trisection of the line segment joining the points(4,-8) and (7,4) are

Answer 1

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Answer 2

Answer:

The coordinates of P is (5,4) and Q is (2,0)

Step-by-step explanation:

Given: The coordinate of the point trisection of the line segment joining the points $A(x_1,y_1)=(4,-8)$ and $B(x_2,y_2)=(7,4)$  

Let P and Q are the point of trisection.

To find : The coordinates of the point P and Q.

Solution :

Trisection points are there

So, P divides the line Ab is the ration m:n = 1:2

Then, Using section formula $(x_3,y_3)=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}$

$(x_3,y_3)=\frac{1(7)+2(4)}{1+2},\frac{1(4)+2(-8)}{1+2}$

$(x_3,y_3)=\frac{7+8}{3},\frac{4-16}{3}$

$(x_3,y_3)=(5,4)$

Now, Q also divide AB internally in the ratio 2:1

So, m:n=2:1

$(x_4,y_4)=\frac{2(7)+1(-8)}{2+1},\frac{2(4)+1(-8)}{2+1}$

$(x_4,y_4)=\frac{14-8}{3},\frac{8-8}{3}$

$(x_4,y_4)=(2,0)$

The coordinates of P is (5,4) and Q is (2,0)