Question

find the ratio in which the point x, 2 divide the line segment joining the point (-3,-4) and (3,5). also find the value of x. please fast....

Answer 1

The answer is 1. View the attachment for further explanation.

Answer 2

The point (x, 2) divides the line segment joining (-3, -4) and (3, 5) in the ratio 1: -7

To find the ratio in which the point (x, 2) divides the line segment joining the point (-3, -4) and (3, 5), we can use the section formula.

The section formula states that a point P on a line segment joining A and B, dividing it in the ratio m:n, is given by:

P = $(mB + nA)/(m+n)$

We are given that the point P is (x, 2) and the line segment is joining (-3, -4) and (3, 5).

So, we can write the coordinates of point P as:

$x = (m3 + n-3)/(m+n)$

$2 = (m5 + n-4)/(m+n)$

Now we can solve the system of equation above to find the value of x and m:n ratio:

$x = (m3 + n-3)/(m+n)$

$x = (3m - 3n)/(m+n)$

$2 = (m5 + n-4)/(m+n)$

$2 = (5m - 4n)/(m+n)$

Multiply first equation by (m+n) and second equation by (m+n)

$x*(m+n) = 3m - 3n$

$2*(m+n) = 5m - 4n$

Add the two equations above:

$x*(m+n) + 2*(m+n) = 3m - 3n + 5m - 4n$

$(x+2)*(m+n) = 8m - 7n$

If we divide both sides of the equation by 8, we get:

$(m+n)/8 = m/8 - n/8$

$So, m/(m+n) = 1/8$

and, $n/(m+n) = -7/8$

This means that the point (x, 2) divides the line segment joining (-3, -4) and (3, 5) in the ratio 1: -7

Now we can use the value of x from the first equation:

$x = (3m - 3n)/(m+n)$

$x = (31 - 3-7)/(1 + -7)$

$x = (3 + 21)/(-6)$

$x = -24/-6$

x = 4

So the point (x, 2) divides the line segment joining (-3, -4) and (3, 5) in the ratio 1: -7

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