Question

find the coordinates of the points which divide the line segment joining (4,-3) and (8,5) and ratio 3:1 internally​

Answer 1

AnswEr:-

Your Answer is (7,3)

ExplanaTion:-

Given:-

• Al line segment joiningthe coordinates (4,3) and (8,5).

To Find:-

• The coordinates of point which divides the given line segment in ratio 3:1 internally.

So,

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

Formula Used:-

• Section Formula,

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

Where,

• $\tt m_1 \:\:And\:\:m_2$ is the given ratio.

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

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

So Here,

$\tt\longrightarrow x_1\:\:And\:\:x_2$ are 4 and 8 respectively.

$\tt\longrightarrow y_1\:\:And\:\:y_2$ are -3 and 5 respectively.

$\tt\longrightarrow m_1\:\:And\:\:m_2$ are 3 and 1 respectively.

Now, lets find out the coordinates of the point by applying section Formula:-

$\\ \tt\mapsto X = \dfrac{3(8)+1(4)}{3+1} \\ \\ \tt\mapsto X = \dfrac{24+4}{4} \\ \\ \tt\mapsto X = \dfrac{\cancel{28}}{\cancel{4}} \\ \\ \tt\mapsto X = 7.$

Similarly,

$\\ \tt\mapsto Y = \dfrac{3(5)+1(-3)}{3+1} \\ \\ \tt\mapsto Y = \dfrac{15+(-3)}{4} \\ \\ \tt\mapsto Y = \dfrac{15-3}{4} \\ \\ \tt\mapsto Y = \dfrac{\cancel{12}}{\cancel{4}} \\ \\ \tt\mapsto Y = 3.$

$\tt\therefore$ The required coordinates of the point are (X,Y) = (7,3).

Answer 2

Answer:

(7,3)

Step-by-step explanation:

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