Question

Draw straight lines by joining the points A(2,5) B(-5,-2) M(-5, 4) N(1,-2) also find the point of intersection

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Answer 1

The point of intersection of the two lines AB and MN is (-0.6, 2.6)

To draw straight lines by joining the points A(2,5), B(-5,-2), M(-5,4), N(1,-2) on a Cartesian coordinate plane, we can plot the points and then connect them with a straight line.

A is located at the point (2,5) on the coordinate plane. B is located at the point (-5,-2). M is located at the point (-5, 4) and N is located at the point (1,-2)

AB and MN are two straight lines, we can find the point of intersection of these two lines by solving the system of equations that represents the two lines.

THe equation of the line AB can be written as:

y = m1x + c1

m1 =$(y2-y1)/(x2-x1)$ and $c1 = y1 - m1*x1$

The equation of the line MN can be written as :

$y = m2x + c2$

$m2 = (y4-y3)/(x4-x3)$ and $c2 = y3 - m2*x3$

By substituting the values of x1,y1,x2,y2,x3,y3,x4 and y4 in the equation we can find the values of m1,c1,m2 and c2

Now we can equate these two equations to find the point of intersection (x,y)

$x = (c2-c1)/(m1-m2)$

$y = m1x + c1$

So the point of intersection of the two lines AB and MN is (-0.6, 2.6)

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Answer 2

The point of intersection of these lines is (3,6)

Ginen: The points of lines are A(2,5) B(-5,-2) and M(-5, 4) N(1,-2)

To Find: Point of intersection of line

Solution:

Equation of line AB = (y-y1) = m(x-x1)

Equation of line = x-y = -3 i)

Equation of line MN = x+y = 9 ii)

x = -3+y  

put it in equation ii)

Now, after solving the two equation we get y = 6 and x = 3

Hence, the point of intersection of two lines is (3,6).

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