Solve sub-questions:Show that ABCD is a parallelogram if A = (4, 8), B = (5, 5), C = (2, 4), D = (1, 7)

Question

Philoid · Accepted Answer

Given: A = (4, 8), B = (5, 5), C = (2, 4), D = (1, 7)

To Prove: AD||BC

AB||DC

Proof:

Let A (4,8) = (x₁, y₁); B (5,5) = (x₂, y₂);

C (2,4) = (x₃, y₃) and D (1,7) = (x₄, y₄)

Distance between two points P (x₁, y₁) and Q (x₂, y₂) =

The slope of the line AB = [Distance formula]

=

= …(i)

The slope of the line DC = [Distance formula]

=

= …(ii)

The slope of the line AD = [Distance formula]

=

= …(iii)

The slope of the line BC = [Distance formula]

=

The slope of line AB = The slope od’s the line DC [From (1) and (2)]

∴ AB||DC

The slope of line AD = The slope of the line BC [From(3) and (4)]

∴ AD||BC

Hence, ABCD is a parallelogram.

Solve sub-questions:
Show that ABCD is a parallelogram if A = (4, 8), B = (5, 5), C = (2, 4), D = (1, 7)