Question

9. Without using the distance formula, show
that the points A (4.5), B (1, 2), C (4.
and D (7. 6) are the vertices of a
parallelogram​

Answer 1

Step-by-step explanation:

Given points are A(4,5),B(1,2),C(4,3) and D(7,6).

Slope of AB=

(1–4)

(2–5)

=−

−3

3

=1

Slope of CD=

(7–4)

(6–3)

=

3

3

=1

As the slope of AB = slope of CD

So, we can conclude AB∥CD

Now,

Slope of BC=

(4–1)

(3–2)

=

3

1

Slope of DA=

(4–7)

(5–6)

=−

−3

1

=

3

1

As, slope of BC = slope of DA

Hence, we can say BC∥DA

Therefore, ABCD is a parallelogram.