Question

Find the coordinates of the point which divides the line segment joining the points (4 3) and (4 -5)in the ratio 3:1

Answer 1

Solution :-

To Find :-

Coordinates of the point which divides the line segment joining ( 4 , 3 ) and ( 4 , -5 ) in the ratio 3 : 1 .

We can find the coordinates of the point using section formula.

According to section formula :-

$\bullet \bf \ x \ coordinate = \dfrac{mx_2+nx_1} {m+n} \\\\\bullet \ y \ coordinate = \dfrac{my_2+ny_1}{m+n}$

Here :-

$\bullet \sf \ x_1=4 \ , \ x_2 = 4 \\\\\bullet \ y_1=4 \ , y_2 = -5 \\\\\bullet \ m = 3 \ , \ n=1$

x coordinate :-

$\longrightarrow \sf \dfrac{(3 \times 4 ) +( 1 \times 4)}{3+1} \\\\\longrightarrow \dfrac{12+4}{4} \\\\\longrightarrow \dfrac{16}{4}\\\\\longrightarrow \bf 4$

y coordinate :-

$\longrightarrow \sf \dfrac{(3 \times -5)+ (1 \times 3)}{3+1} \\\\\longrightarrow \dfrac{-15+3}{4} \\\\\longrightarrow \dfrac{-12}{4} \\\\\longrightarrow \bf -3$

Coordinates of the point = ( 4 , -3 )

Answer 2

Answer:

To Find :-

Coordinates of the point which divides the line segment joining ( 4 , 3 ) and ( 4 , -5 ) in the ratio 3 : 1 .

We can find the coordinates of the point using section formula.

According to section formula :-

$∙ x coordinate=m+nmx2+nx1∙ y coordinate=m+nmy2+ny1$

$Here :-</p><p></p><p>\begin{gathered}\bullet \sf \ x_1=4 \ , \ x_2 = 4 \\\\\bullet \ y_1=4 \ , y_2 = -5 \\\\\bullet \ m = 3 \ , \ n=1\end{gathered}∙ x1=4 , x2=4∙ y1=4 ,y2=−5∙ m=3 , n=1</p><p></p><p>x coordinate :-</p><p></p><p>\begin{gathered}\longrightarrow \sf \dfrac{(3 \times 4 ) +( 1 \times 4)}{3+1} \\\\\longrightarrow \dfrac{12+4}{4} \\\\\longrightarrow \dfrac{16}{4}\\\\\longrightarrow \bf 4\end{gathered}⟶3+1(3×4)+(1×4)⟶412+4⟶416⟶4</p><p></p><p>$

$y coordinate :-</p><p></p><p>\begin{gathered}\longrightarrow \sf \dfrac{(3 \times -5)+ (1 \times 3)}{3+1} \\\\\longrightarrow \dfrac{-15+3}{4} \\\\\longrightarrow \dfrac{-12}{4} \\\\\longrightarrow \bf -3\end{gathered} </p><p>⟶ </p><p>3+1</p><p>(3×−5)+(1×3)</p><p> </p><p> </p><p>⟶ </p><p>4</p><p>−15+3</p><p> </p><p> </p><p>⟶ </p><p>4</p><p>−12</p><p> </p><p> </p><p>⟶−3$