Question

Find the ratio in which the point (-3, k) divides the line-segment joining the points (-5, -4) and (-2, 3). Also find the value of k.
If the point C (-l, 2) divides internally the line-segment joining the points A (2, 5) and
B (x,y) in the ratio 3 : 4, find the value of x2 + y2.

Answer 1

Step-by-step explanation:

given A(-5,-4), B(-2,3), P(-3,k)

ratio = x- x1:x2-x=-3-(-5):-2-(-3)=-3+5:-2+3=2:1.

(-3,k)=(2(-2)+1(-5)/1+2,2(3)+1(-4)/2+1)

equate the y coordinates

k=6-4/3=2/3......

given A(2 ,5) B(x,y) C(-1,2)

m:n=3:4

(-1,2)=(3(x)+4(2)/3+4,3(y)+4(5)/3+4)

(-1,2)=(3x+8/7,3y+20/7)

-1=3x+8/7,2=3y+20/7

-7=3x+8,14=3y+20

-15=3x,-6=3y

x=-5,y=-2

×^2+y^2=(-5)^2+(-2)^2=25+4=29