Question

Find the ratio in which the point p(2,x) divides the line joining the point A(-2,2) B(3,7) internally .also find the value of x

Answer 1

Answer:

Let the ratio be k:1

So x1=2

2=(3k-2)/(k+1)

2k+2=3k-2

-k=-4

k=4:1

Ratio=4:1

x=(4*7+1*2)/(4+1)

x=(28+2)/5

x=6

Answer 2

Step-by-step explanation:

Let point (2,x) divides the line segment joining the points A(-2,2) B (3,7) internally in k:1.

Section formula:

If a point divides a line segment in m:n whose end points are (x_1,y_1)(x1,y1) and (x_2,y_2)(x2,y2) , then the coordinates of that point are

(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})(m+nmx2+nx1,m+nmy2+ny1)

If point (2,x) divides the segment AB internally in k:1, then

(2,x)=(\frac{(k)(3)+(1)(-2)}{k+1},\frac{(k)(7)+(1)(2)}{k+1})(2,x)=(k+1(k)(3)+(1)(−2),k+1(k)(7)+(1)(2))

(2,x)=(\frac{3k-2}{k+1},\frac{7k+2}{k+1})(2,x)=(k+13k−2,k+17k+2)

On comparing both sides.

2=\frac{3k-2}{k+1}2=k+13k−2

2(k+1)=3k-22(k+1)=3k−2

2k+2=3k-22k+2=3k−2

2k-3k=-2-22k−3k=−2−2

-k=-4−k=−4

k=4k=4

It means point (2,x) divides the segment AB internally in 4:1.

x=\frac{7k+2}{k+1}x=k+17k+2

Substitute k=4.

x=\frac{7(4)+2}{4+1}x=4+17(4)+2

x=\frac{30}{5}x=530

x=6x=6

Therefore, the value of x is 6.