Question

The vertices of a parallelogram are (2, -3) (6, 5) (-2, 1) (-6, -7) in this order. the point of the intersection of the diagonals is​

Answer 1

Answer:

(0 , -1) we will use mid point formula

Answer 2

Note:

This problem can be solved simply just by finding the mid-points of AC and BD since the have their mid-points as the common point for both.

Yet we try to solve the problem using equations for the diagonals.

Step-by-step explanation:

Step 1. drawing a diagram

Refer to the attachment to draw a diagram of the given parallelogram.

Step 2. finding equations of the diagonals

The equation of AC is

$\quad \dfrac{y-1}{1-(-3)}=\dfrac{x-(-2)}{-2-2}$

$\Rightarrow \dfrac{y-1}{1+3}=\dfrac{x+2}{-4}$

⇒ y - 1 = - x - 2

⇒ x + y + 1 = 0 ... ... (i)

The equation of BD is

$\quad \dfrac{y-5}{5-(-7)}=\dfrac{x-6}{6-(-6)}$

$\Rightarrow \dfrac{y-5}{12}=\dfrac{x-6}{12}$

⇒ y - 5 = x - 6

⇒ x = y + 1 ... ... (ii)

Step 3. finding solution of (i) and (ii)

We have two equations:

x + y + 1 = 0 ... ... (i)

x = y + 1 ... ... (ii)

Putting x = y + 1 in (i), we get

y + 1 + y + 1 = 0

⇒ 2y + 2 = 0

⇒ y + 1 = 0

⇒ y = - 1

Putting y = - 1 in (ii), we get

x = - 1 + 1

⇒ x = 0

So the required solution is x = 0, y = - 1

Final answer:

The point of intersection of the diagonals of the given parallelogram is (0, - 1).

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