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Sophie [7]
2 years ago
13

The endpoints of ab are a(1,4) and b(6,-1). If point c divides ab in the ratio 2:3, the coordinates of c are ?. If point d divid

es ac in the ratio 3:2, the coordinates of d are ?.
Mathematics
2 answers:
Luden [163]2 years ago
8 0

Answer:  The co-ordinates of point C are (3, 2) and the co-ordinates of the point D are \left(\dfrac{11}{5},\dfrac{14}{5}\right).

Step-by-step explanation:  Given that the endpoints of a line segment AB are  A(1,4) and B(6,-1).

We are to find the co-ordinates of a point C that divides the line segment AB in the ratio 2 : 3.

Also, to find the co-ordinates of the point D that divides the line segment AC in the ratio 3 : 2.

We know that

the co-ordinate of a point that divides a line segment with endpoints (p. q) and (r, s) in the ratio m : n is given by

\left(\dfrac{mr+np}{m+n},\dfrac{ms+nq}{m+n}\right).

Therefore, the co-ordinates of point C will be

C\\\\\\=\left(\dfrac{2\times 6+3\times 1}{2+3},\dfrac{2\times (-1)+3\times 4}{2+3}\right)~~~~~~~~~~[\textup{here, m : n = 2 : 3}]\\\\\\=\left(\dfrac{12+3}{5},\dfrac{-2+12}{5}\right)\\\\\\=\left(\dfrac{15}{5},\dfrac{10}{5}\right)\\\\=(3,2).

And, the co-ordinates of the point D will be

D\\\\\\=\left(\dfrac{3\times 3+2\times 1}{3+2},\dfrac{3\times 2+2\times 4}{3+2}\right)~~~~~~~~~~[\textup{here, m : n = 3 : 2}]\\\\\\=\left(\dfrac{9+2}{5},\dfrac{6+8}{5}\right)\\\\\\=\left(\dfrac{11}{5},\dfrac{14}{5}\right).

Thus, the co-ordinates of point C are (3, 2) and the co-ordinates of the point D are \left(\dfrac{11}{5},\dfrac{14}{5}\right).

aliya0001 [1]2 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

Find the coordinates of c using the section formula

x_{c} = \frac{(3(1)+(2(6)}{2+3} = \frac{3+12}{5} = 3

y_{c} = \frac{(3(4))+(2(-1))}{2+3} = \frac{12-2}{5} = 2

coordinates of c = (3, 2)

Similarly to find the coordinates of d

x_{d} = \frac{x(2(1))+(3(3))}{3+2} = \frac{2+9}{5} = \frac{11}{5}

y_{d} = \frac{(2(4))+(3(2))}{3+2} = \frac{8+6}{5} = \frac{14}{5}

coordinates of d = ( \frac{11}{5}, \frac{14}{5})


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