Question

The co-ordinates of the mid-points of the line joining P(-12,14) and (14,-12) are :
a)(0,0) b) (1,1) c) (1,0) d) (-1,0)

Answer 1

Answer:

• b) (1, 1)

Explanation:

Given coordinates,

• P(-12, 14)
• Q(14, -12)

Using the midpoint formula,

$= \bigg(\boldsymbol{\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}} \bigg)$

Where,

• $x_1 \: {\rm and}\: y_1$ are the coordinates of P.
• $x_2 \: {\rm and}\: y_2$ are the coordinates of Q.

Substitute the given coordinates,

$= \bigg({\dfrac{( - 12) + 14}{2}, \dfrac{14 + ( - 12)}{2}} \bigg)$

$= \bigg({\dfrac{- 12 + 14}{2}, \dfrac{14 - 12}{2}} \bigg)$

$= \bigg({\dfrac{2}{2}, \dfrac{2}{2}} \bigg)$

$= (1, \: 1)$

∴ Mid-point of the points P and Q is (1, 1).

__________________________

Answer 2

Answer:

Appropriate Question :-

• The co-ordinates of the mid-point of the line joining P(- 12 , 14) and Q(14 , - 12) are :

Options :

● (a) (0 , 0)

● (b) (1 , 1)

● (c) (1 , 0)

● (d) (- 1 , 0)

Given :-

• The co-ordinates are P(- 12 , 14) and Q(14 , - 12).

To Find :-

• What is the mid-point.

Formula Used :-

$\clubsuit$ Mid-Point Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Mid-Point =\: \bigg[\dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2}\bigg]}}}\: \: \: \bigstar$

where,

• (x₁ , y₁) = Co-ordinates of the first point
• (x₂ , y₂) = Co-ordinates of the second point

Solution :-

Given Co-ordinates :

$\mapsto \bf P(- 12 , 14)$

$\mapsto \bf Q(14 , - 12)$

where,

• x₁ = - 12
• y₁ = 14
• x₂ = 14
• y₂ = - 12

According to the question by using the formula we get,

$\implies \bf Mid-Point =\: \bigg[\dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2}\bigg]$

$\implies \sf Mid-Point =\: \bigg[\dfrac{- 12 + 14}{2} , \dfrac{14 + (- 12)}{2}\bigg]$

$\implies \sf Mid-Point =\: \bigg[\dfrac{2}{2} , \dfrac{14 - 12}{2}\bigg]$

$\implies \sf Mid-Point =\: \bigg[\dfrac{\cancel{2}}{\cancel{2}} , \dfrac{\cancel{2}}{\cancel{2}}\bigg]$

$\implies \sf Mid-Point =\: \bigg[\dfrac{1}{1} , \dfrac{1}{1}\bigg]$

$\implies \sf Mid-Point =\: [1 , 1]$

$\implies \sf\bold{\red{Mid-Point =\: (1 , 1)}}$

$\sf\bold{\purple{\underline{\therefore\: The\: mid-point\: is\: (1 , 1)\: .}}}$

Hence, the correct options is option no (b) (1 , 1) .

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

EXTRA INFORMATION :-

$\clubsuit$ Distance Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Distance =\: \sqrt{\bigg(x_2 - x_1\bigg)^2 + \bigg(y_2 - y_1\bigg)^2}}}}\: \: \: \bigstar$

$\clubsuit$ Section Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Section =\: \bigg\lgroup \dfrac{m_1x_2 + m_2x_1}{m_1 + m_2} , \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2}\bigg\rgroup}}}\: \: \: \bigstar$

$\clubsuit$ Centroid Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Centroid =\: \bigg\lgroup \dfrac{x_1 + x_2 + x_3}{3} , \dfrac{y_1 + y_2 + y_3}{3}\bigg\rgroup}}}\: \: \: \bigstar$

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃