Question

Point p divides the line segment joining the points A(2,1) and (5,-8) such that AP/BP = 1/3 if p lies on the line 2x-y+k=0 find k

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

A(2,1)------------------P(x,y)-----------------------B(5,-8)

here, the ratio given is AP/BP = 1/3, so, using the formula:

         (m1(x1) + m2(x2)/m1+m2, m1(y1) + m2(y2)/m1+m2) = P(x,y)

        [1(5) + 3(2)/3+1, 1(-8) + 3(1)/3+1] = P(x,y)

  x= 5+6/4 = 11/4

  y= -8+3/4 = -5/4

therefore, P(11/4, -5/4)

now, we substitute the values of x and y on the equation 2x-y+k to find k:

      2(11/4) - (-5/4) + k = 0

      11/2 + 5/4 + k =0

      22+5+4k = 0

      27 + 4k=0

      4k = -27

      k = -27/4

so, we get k as -27/4