In each of the following examples find the co-ordinates of point A which divides segment PQ in the ratio a: b.P(-2, -5), Q(4, 3), a ः b = 3: 4

Explanation:-

We are given a point P which is the intersection of two lines, and we need to find the coordinates of P. We can use the formula for finding the point of intersection of two lines, which is:

x = (b2 – b1)/(m1 – m2) y = m1x + b1

Where (x,y) is the point of intersection, m1 and m2 are the slopes of the two lines, and b1 and b2 are the y-intercepts of the two lines.

We are not given the equations of the lines, but we can find the slopes and y-intercepts from the given points (3,4) and (-2,-5) that lie on the lines.

The slope of the first line can be found as:

m1 = (4 – (-5))/(3 – (-2)) = 9/5

The y-intercept of the first line can be found by substituting one of the given points into the equation of the line:

y = mx + b 4 = (9/5)3 + b b = 4 – (9/5)3 = 7/5

So, the equation of the first line is y = (9/5)x + 7/5.

Similarly, the slope of the second line can be found as:

m2 = (-5 – 4)/(-2 – 3) = 9/5

The y-intercept of the second line can be found using the other given point:

y = mx + b -5 = (9/5)(-2) + b b = -5 – (9/5)(-2) = -1/5

So, the equation of the second line is y = (9/5)x – 1/5.

Now we can use the formula for finding the point of intersection:

x = (b2 – b1)/(m1 – m2) y = m1x + b1

Substituting the values we found above, we get:

x = (-1/5 – 7/5)/(9/5 – 9/5) = -8/0 (undefined)

Since the denominator is zero, the value of x is undefined. This means that the lines are parallel and do not intersect.

Therefore, there is no point of intersection and we cannot find the coordinates of P.