Question

Show that the line joining (2, – 3) and (- 5, 1) is:
(i) Parallel to line joining (7, -1) and (0, 3).
(ii) Perpendicular to the line joining (4, 5) and (0, -2).

Answer 1

Let m1 be the slope of line joining (2, -3) and (-5, 1) then
m₁ = `(Y-2 - y_1)/(x_2 - x_1)`
= `(1 - (-3))/(-5 - 2) = -(4)/(7)`
(i) Let m₂ be the slope of the line joining (7, -1) and (0, 3), then
m₂ = `(3 - (-1))/(0, 7) = -(4)/(7)`
Since, m₁ = m₂, the two lines are parallel.
Hence proved.
(ii) Let m₃ be the slope of the line joining (4, 5) and (0, -2) then
m₃ = `(-2 - 5)/(0 - 4) = (7)/(4)`
Now m₁m₃ = `-(4)/(7) xx (7)/(4)` = -1
Hence, the two lines are perpendicular.
Hence proved.