Question

Find k, if PQ||RS and P(2,4), Q (3,6), R(3,1), S(5,k) .

Answer 1

it is given that, PQ || RS, means line PQ is parallel to line RS.

it is possible only if,

• slope of line PQ = slope of line RS

we know, if two points are given A(x1, y1) and B(x2, y2) then, slope of AB = (y2 - y1)/(x2 - x1)

so, slope of line PQ = (6 - 4)/(3 - 2) = 2/1=2

slope of line RS = (k - 1)/(5 - 3) = (k - 1)/2

now, 2 = (k - 1)/2

⇒2 × 2 = k - 1

⇒4 + 1 = k

⇒k = 5

hence, value of k = 5