Question

The coordinates of the midpoint P, which divides the line segment joining the points P(2, – 4) and Q(– 4, 3) are A. [–1, –(1/2)]. B. [ 1, – (1/2)]. C. [– 3, (7/2)]. D. [3, –(7/2)].

Answer 1

AnswEr:-

Your Answer Is Option A) $\bf[-1,\:\: -(\dfrac{1}{2})].$

ExplanaTion:-

Given:-

• The Coordinates of two points which are joined to make a line segment PQ.

• The coordinates are P(2, -4) and Q(-4, 3).

To Find:-

• The midpoint of the line segment.

Formula Used:-

Mid Point Formula:-

$\bf\longrightarrow X = \dfrac{x_1 +x_2}{2} .$

$\bf\longrightarrow Y = \dfrac{y_1 + y_2}{2}.$

Where,

• X and Y are coordinates of the mid point.

• $\tt x_1$ And $\tt x_2$ Are the x coordinates of the points joining the line segment.

• $\tt y_1$ And $\tt y_2$ Are the y coordinates of the points joining the line segment.

So Here,

• X and Y = ?? [To Find].

• $\tt x_1$ And $\tt x_2$ = 2 and -4 respectively.

• $\tt y_1$ And $\tt y_2$ = -4 and 3 respectively.

Now,

By putting the above values in formula,

$\tt\mapsto \: X = \dfrac{x_1 + x_2}{2} .$

$\tt\mapsto \: X = \dfrac{2 + ( - 4)}{2} .$

$\tt\mapsto \: X = \dfrac{2 - 4}{2}.$

$\tt\mapsto \: X = - \dfrac{ 2}{2}.$

$\bf\mapsto \boxed{ \bf \: X = - 1.}$

Similarly,

$\tt\mapsto \: Y = \dfrac{y_1 + y_2}{2} .$

$\tt\mapsto \: Y = \dfrac{ - 4 + 3}{2} .$

$\bf\mapsto \boxed{ \bf \: Y = - \dfrac{1}{2}.}$

Therefore,

The coordinates of the midpoint are (X, Y) $\bf =[-1,\:\:-(\dfrac{1}{2})].$

And Hence The Final Answer Is Option A.