Question

3. Find the coordinates of the pointowhere the diagonals of the parallelogran formed by
joining the points (-2,-1), (1,0), (4,3) and (1,2) meet
​

Answer 1

Answer:

(1,1)

Step-by-step explanation:

The vertices of parallelogram in order are A(−2,−1),B(1,0),C(4,3),D(1,2).

So the diagonals will be AC and BD.

Since the diagonals of a parallelogram bisects each other, so mid-point of

AC or BD will be intersection point of diagonals.

Hence by mid-point theorem, mid-point of AC is

A(−2,−1) and C(4,3)

x=

2

−2+4

=1 and y=

2

−1+3

=1.

so (1,1) is required point.

Answer 2

We're given the points (−2,−1), (1,0), (4,3) and (1,2). And by joining this points with respect to diagonal a parallelogram is formed.

Here, let's assume that the vertices of the parallelogram are A(-2,-1), B(1,0), C(4,3), D(1,2) respectively.

⋆ Diagram is given below :

$\setlength{\unitlength}{1cm}\begin{picture}(21,15)\thicklines\qbezier(1,1)(1,1)(7,1)\qbezier(1,1)(1,1)(2,4)\qbezier(7,1)(7,1)(8,4)\qbezier(8,4)(8,4)(2,4)\qbezier(8,4)(8,4)(1,1)\qbezier(2,4)(2,4)(7,1)\put(0.6,0.5){\sf D(1,2)}\put(7,0.5){\sf C(4,3)}\put(8,4.3){\sf B(1,0)}\put(1,4.3){\sf A(- 2,- 1)}\put(4.2,3){\large\sf O(x,y)}\end{picture}$

By using mid point formula,

$\longrightarrow\sf \: Mid \: point = \Bigg( \dfrac{x_1 + x_2}{2} ,\dfrac{y_1 + y_2}{2}\Bigg)$

Substituting the values,

$\longrightarrow\sf \: Mid \: point \: of \: AC= \Bigg( \dfrac{ - 2 + 4}{2},\dfrac{ - 1 + 3}{2}\Bigg)$

$\longrightarrow\sf \: Mid \: point \: of \: AC= \Bigg( \dfrac{ 2}{2},\dfrac{ 2}{2}\Bigg)$

$\longrightarrow\sf \: { \underline{ \boxed{ \purple{ \frak{Mid \: point \: of \: AC= \big(1,1 \big)}}}}} \: \: \bigstar$

Therefore, the required coordinate is (1, 1).

$\: \: \: \: \:\star\Large{\underline{\underline{\frak{\pink{Additional\: information :}}}}}$

• The Midpoint Formula is used to find out the precise center point between two defined points during a line segment.

• One should use this formula to calculate the point that bisects a line segment.

$\large \: {\boxed{\sf{Mid \: point \: = \Bigg( \dfrac{x_1 + x_2}{2} ,\dfrac{y_1 + y_2}{2}\Bigg) }}}$