Question

P is the point with coordinates (2, 3).

Q is the point with coordinates (12, 7).

Work out the coordinates of the midpoint of the line PQ

Answer 1

Answer:

• (7, 5)

Explanation:

Given points,

• P(2, 3)
• Q(12, 7)

Using mid-point formula,

$\boldsymbol{ = \dfrac{x_1 + x_2}{2} \: \dfrac{y_1 + y_2}{2} }$

Where,

• $\boldsymbol {x_1,\: y_1}$ denotes the coordinates of P.
• $\boldsymbol {x_2,\: y_2}$ denotes the coordinates of Q.

Substituting the given coordinates,

$= \bigg( \dfrac{[2 + 12]}{2},\: \dfrac{[3 + 7]}{2} \bigg)$

$= \bigg( \dfrac{14}{2},\: \dfrac{10}{2} \bigg)$

$= \big( 7,\: 5 \big)$

∴ Midpoint of P, Q is (7, 5)

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Answer 2

Answer:

Given :-

• P is the point with co-ordinates (2 , 3).
• Q is the point with co-ordinates (12 , 7).

To Find :-

• What is the co-ordinates of the mid-point of the line PQ.

Formula Used :-

$\clubsuit$ Mid-Point Formula :

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

where,

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

Solution :-

Given Co-ordinates :

$\leadsto \sf P(2 , 3)$

$\leadsto \sf Q(12 , 7)$

where,

• x₁ = 2
• y₁ = 3
• x₂ = 12
• y₂ = 7

According to the question by using the formula we get,

$\implies \bf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2}\bigg\}$

$\implies \sf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{2 + 12}{2} , \dfrac{3 + 7}{2}\bigg\}$

$\implies \sf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{\cancel{14}}{\cancel{2}} , \dfrac{\cancel{10}}{\cancel{2}}\bigg\}$

$\implies \sf Mid-Point_{(P , Q)} =\: \bigg\{\dfrac{7}{1} , \dfrac{5}{1}\bigg\}$

$\implies \sf\bold{Mid-Point_{(P, Q)} =\: (7 , 5)}$

$\therefore$ The mid-point of the co-ordinates of the line PQ is (7 , 5) .