Question

This question is very difficult

Answer 1

Explanation:

Let D divide the line between (-4,3) and (2,7) in the ratio m:n

Let the coordinates of D be (x,y).

As D lies on the y- axis, x=0.

Use the formula: x=
`0=((-4)(n)+(2(m))/(m+n)`

Solve to get m=2n.

Therefore, the line is divided in the ratio 1:2

`y=(3(2)+7(1))/(1+2)`

Therefore, y=13/3

Therefore D=(0,13/3)

Answer 2

(0, 17/3)

Explanation:

Look at (2,7) and (-4,3)

Slope of the line going through 2 points are:

m = (y2 - y1)/(x2 - x1) = (3 - 7)/(-4 - 2) = -4/-6 = 2/3

Using m = 2/3, y =7, x = 2

y = mx + b

=> 7 = 2/3(2) + b

7 = 4/3 + b

b = 7 - 4/3 = 21/3 - 4/3 = 17/3

so equation of the line going through (2,7) and (-4,3) is:

y = 2/3x + 17/3

D is on y-axis which means x = 0

so y = 2/3 (0) + 17/3 => y = 17/3

then D is (0, 17/3)

Hope this helps.