THE LINE V PASSES THROUGH THE POINTS(-5,3)&(7,-3)&THE LINE W PASSES THROUGH THE POINTS (2,-4)&(4,2).THE LINE V&W INTERSECT AT THE POINT A.WORK OUT THE COORDINATES OF THE POINT A

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Find equation of line V

(y-3)/(x+5)= (-6/12)
-6 x - 30 = 12 y - 36
12 y = -6 x + 6
6 y = -3 x + 3
Find equation of line W
(y+4)/(x-2) = 6/2 = 3
3 x - 6 = y + 4
y = 3 x - 10
Find intersection
6 y = -3 x + 3
1 y = +3 x - 10
--------------
7 y = -0 x - 7
y = -1
-7 = 3 x - 10
3 x = 3
x = 1
so
(1,-1)

To find the coordinates of the point where the two lines intersect, you can solve the equations of the two lines simultaneously. Given the points, you can determine the slope of each line and then find the equation of each line in the slope-intercept form (y = mx + c). Once you have the equations, you can solve them to find the coordinates of the point of intersection.

Let's start by finding the equation of line V:
The slope of line V is given by the formula:
m = (y2 - y1)/(x2 - x1), where (x1, y1) = (-5, 3), and (x2, y2) = (7, -3).

Substituting the values, we get:
m = (-3 - 3)/(7 - (-5))
m = (-6)/(7 + 5)
m = -6/12
m = -1/2

Using the point-slope form, the equation of line V becomes:
y - y1 = m(x - x1)
y - 3 = (-1/2)(x - (-5))
y - 3 = (-1/2)(x + 5)
y - 3 = (-1/2)x - 5/2
y = (-1/2)x - 5/2 + 3
y = (-1/2)x - 5/2 + 6/2
y = (-1/2)x + 1/2

Next, let's find the equation of line W:
The slope of line W is given by the formula:
m = (y2 - y1)/(x2 - x1), where (x1, y1) = (2, -4), and (x2, y2) = (4, 2).

Substituting the values, we get:
m = (2 - (-4))/(4 - 2)
m = 6/2
m = 3

Using the point-slope form, the equation of line W becomes:
y - y1 = m(x - x1)
y - (-4) = 3(x - 2)
y + 4 = 3(x - 2)
y + 4 = 3x - 6
y = 3x - 6 - 4
y = 3x - 10

Now you have the equations of both lines: Line V = y = (-1/2)x + 1/2 and Line W = y = 3x - 10.

To find the point of intersection, set the two equations equal to each other:
(-1/2)x + 1/2 = 3x - 10

Let's solve this equation:

(-1/2)x - 3x = -10 - 1/2
(-1/2 - 6/2)x = -10 - 1/2
(-7/2)x = -20 - 1/2
(-7/2)x = -41/2

Now, by cross-multiplication:
x = (-41/2) / (-7/2)
x = (-41/2) * (-2/7)
x = 41/7

Substituting the value of x back into either of the two equations:
y = (-1/2)(41/7) + 1/2
y = -41/14 + 7/14
y = -34/14
y = -17/7

Hence, the coordinates of the point of intersection A are (41/7, -17/7).