Find the ratio in which the point (3, p) divides the line segment join

1.	Find the ratio in which the point (3, p) divides the line segment joining the points (-5,-4) asd(2, 3). Hence, find the value of p.
Answer» solution (x₁,y₁)=(-5,-4), (x₂,y₂) = (-2,3)(-3,p) is the point which divides joining the above points in the ratio k:1by using section formula [(k(-2)+15)/(k+1) , (k3+1(-4))/(k+1)] = (-3,p)equating x co ordinates(-2k+5)/(k+1) = -3-2k+5 = -3(k+1)-2k+5 = -3k-3-2k+3k=-3-5k= -8---(1) equating y co ordinates(3k-4)/(k+1) = psubstitute k = -8 [3*(-8) -4]/(-8+1) = p (-24-4)/-7 = p-28/-7 =p4=pp=4

Find the ratio in which the point (3, p) divides the line segment joining the points (-5,-4) asd(2, 3). Hence, find the value of p.

Answer»

solution

(x₁,y₁)=(-5,-4), (x₂,y₂) = (-2,3)(-3,p) is the point which divides joining the above points in the ratio k:1by using section formula

[(k*(-2)+1*5)/(k+1) , (k*3+1*(-4))/(k+1)] = (-3,p)equating x co ordinates(-2k+5)/(k+1) = -3-2k+5 = -3(k+1)-2k+5 = -3k-3-2k+3k=-3-5k= -8---(1)

equating y co ordinates(3k-4)/(k+1) = psubstitute k = -8 [3*(-8) -4]/(-8+1) = p

(-24-4)/-7 = p-28/-7 =p4=pp=4