Question

Find k so that the point P(-4,6)lies on the line segment joining the points A(k,10) and B(3,-8). Also, find the ratio in which P divides AB.


Plz help ...❣️❣️

Answer 1

Answer:

Step-by-step explanation:

Find k so that the point p(-4 6) lies on the line segment joining a(k,0),b(3,-8).also find the ratio in which p divides.

Slope using points p and b

Slope = (6- -8)/(-4-3) = 14/-7 = -2

Slope using point a and p

Slope = (6-0)/(-4-k) = -2

6 = 8+2k

2k = -2

k = -1

ab = √(6²+3² = 3√5

pb = √14²+7² = 7√5

∴ap:pb = 3√5 : 7√5 = 3 : 7

Answer 2

☺⭐HERE IS YOUR ANSWER⭐☺

1) we know that the equation of line with 2 points.
is - (y-y1)= Y2-Y1/X2-X1(X-X1)

⭐LET PT. - A(K,10) = (x1,y1)
B(3,-8) = (X2,Y2)

SO, EQUATION =
Y-10 = -8-10/3-K(X-K)
⭐Y-10 = -18/3-K(X-K) ------(1)

⭐NOW,, ACCORDING TO QUS pt. P(-4,6) lies on eq. - (1)

so, we put x = -4 & y = 6
now., 6-10= -18/3-K(-4-K)
-4(3-K) = 18(4+k)
-12+4k = 72+18k
-84 = 14k
(k = -6)

2) let p divides AB in 1:m
then -
⭐by section formula -
-4 = 1(-6) + m(3)/m+1
-4m-4 = -6+3m
so ,, m = 2/7
so, the ratio will be = 2:7 ans..

☺⭐hope it helps u⭐☺