Question

Find the coordinates that partitions (-8,-2) and (6, 19) with the ration 5:2

Answer 1

Explanation:

Using the section formula , if a point ( x , y ) divides the line joining the points ( x1 , y1 ) and ( x2 , y2 ) into the ratio m : n , then

( x , y ) = ( mx2 + nx1 / m + n , my2 + ny1 / m + n)

Let the points be A(-8,−2) and B(6,19). Let a point P(x,y) divides AB in the ratio 5:2

Therefore, we have

`P(x,y) =( (5 * 6 + 2 * - 8)/(5 + 2) , \: (5 * 19 + 2 * - 2)/(5 + 2))`

`P(x,y) = ( (30 + ( - 16))/(7) , \: (95 + ( - 4))/(7) )`

`P(x,y) = (2, 13)`

Answer 2

(2, 13)

Explanation:

Let P be the point that partitions the segment.

Let M = (-8, -2)

Let N = (6, 19)

If point P partitions the segment MN in a 5 : 2 ratio, then to calculate the x and y values of point P:

• divide the difference of the x (or y) values of the two endpoints by the sum of the ratios

• multiply this by 5, since P partitions the segment at 5 : 2
• add this to the x (or y) value of point M

x-value of P:

`\sf \implies \left((x_N-x_M)/(5+2)\right)\cdot5+x_N`

`\sf \implies \left((6-(-8))/(5+2)\right)\cdot5+(-8)=2`

y-value of P:

`\sf \implies \left((y_N-y_M)/(5+2)\right)\cdot5+y_N`

`\sf \implies \left((19-(-2))/(5+2)\right)\cdot5+(-2)=13`

`\sf P=(2,13)`