Question

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

Answer 1

Answer:

(2, 13)

Step-by-step 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:

$\sf \implies \left(\dfrac{x_N-x_M}{5+2}\right)\cdot5+x_N$

$\sf \implies \left(\dfrac{6-(-8)}{5+2}\right)\cdot5+(-8)=2$

y-value of P:

$\sf \implies \left(\dfrac{y_N-y_M}{5+2}\right)\cdot5+y_N$

$\sf \implies \left(\dfrac{19-(-2)}{5+2}\right)\cdot5+(-2)=13$

$\sf P=(2,13)$

Answer 2

Step-by-step 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

$P(x,y) =( \frac{5 \times 6 + 2 \times - 8}{5 + 2} , \: \frac{5 \times 19 + 2 \times - 2}{5 + 2})$

$P(x,y) = ( \frac{30 + ( - 16)}{7} , \: \frac{95 + ( - 4)}{7} )$

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