Question

Find the coordinates of the point which divides the join of P(-5, 11) and
Q(4, -7) in the ratio 7 : 2.

Answer 1

AnswEr:-

Your Answer is (2, -3).

Given:-

• Coordinates of the points joining line segment = p(-5,11) and Q(4,-7).

• The line segment divided by a point in ratio 7:2.

To Find:-

• The coordinates of the point which divides the line segment in ratio 7:2.

Formula Used:-

Section Formula:-

$\\ \\ \tt\longrightarrow X = \dfrac{m_1x_2+m_2x_1}{m_1+m_2}. \\ \\ \tt\longrightarrow Y = \dfrac{m_1y_2+m_2y_1}{m_1+m_2}.$

Where,

• X and Y are coordinates of the point which divides the line segment.

• $\tt m_1 \:\:And\:\:m_2$ are the ratio in which the point (X,Y) divides the line segment.

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

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

So Here,

• $\tt x_1\:\:And\:\:x_2$ are -5 and 4 respectively.

• $\tt y_1\:\:And\:\:y_2$ are 11 and -7 respectively.

• $\tt m_1\:\:And\:\:m_2$ are 7 and 2 respectively.

• And let the coordinates of the point be (X,Y).

So let us apply the above formula to find the value of X and Y:-

$\\ \\ \tt\mapsto X = \dfrac{m_1x_2+m_2x_1}{m_1+m_2}. \\ \\ \tt\mapsto X = \dfrac{7(4)+2(-5)}{7+2}.\\ \\ \tt\mapsto X = \dfrac{28+(-10)}{9}. \\ \\ \tt\mapsto X = \dfrac{28-10}{9}. \\ \\ \tt\mapsto X = \dfrac{\cancel{18}}{\cancel9}.\\ \\ \tt\mapsto X = 2.$

Similarly,

$\\ \\ \tt\mapsto Y = \dfrac{m_1y_2+m_2y_1}{m_1+m_2} \\ \\ \tt\mapsto Y = \dfrac{7( - 7) + 2(11)}{7 + 2}. \\ \\ \tt\mapsto Y = \dfrac{ ( - 49) + 22}{9} . \\ \\ \tt\mapsto Y = \dfrac{ - 49 + 22}{9} . \\ \\ \tt\mapsto Y = - \frac{\cancel{ 27}}{\cancel9} . \\ \\ \tt\mapsto Y = - 3.$

$\tt \therefore$ The coordinates of the point are (X,Y)

= (2, -3).