Question

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.

Answer 1

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

Answer:

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

Step-by-step explanation: