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Sagot :
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
[tex]P(x,y) =( \frac{5 \times 6 + 2 \times - 8}{5 + 2} , \: \frac{5 \times 19 + 2 \times - 2}{5 + 2}) [/tex]
[tex]P(x,y) = ( \frac{30 + ( - 16)}{7} , \: \frac{95 + ( - 4)}{7} )[/tex]
[tex] P(x,y) = (2, 13)[/tex]
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:
[tex]\sf \implies \left(\dfrac{x_N-x_M}{5+2}\right)\cdot5+x_N[/tex]
[tex]\sf \implies \left(\dfrac{6-(-8)}{5+2}\right)\cdot5+(-8)=2[/tex]
y-value of P:
[tex]\sf \implies \left(\dfrac{y_N-y_M}{5+2}\right)\cdot5+y_N[/tex]
[tex]\sf \implies \left(\dfrac{19-(-2)}{5+2}\right)\cdot5+(-2)=13[/tex]
[tex]\sf P=(2,13)[/tex]
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