Answer:
The point of intersection of both diagonals is (0,1)
Explanation:
for the parallelogram, we have the diagonals GJ and HK
Firstly, we need to get the equation of the lines that join these two points
For GJ
the general equation is;
y = mx + b
m is slope and b is y-intercept
We have the points
(-2,3) and (2,-1)
The slope m is as follows;
m = (y2-y1)/(x2-x1)
m = (-1-3)/(2-(-2) = -4/4 = -1
So we have;
y = -x + b
To get b, we substitute any of the two points
Let us use (-2,3)
x = -2 and y = 3
so we have;
3 = -1(-2) + b
3 = 2 + b
b = 3-2 = 1
so we have the equator GJ as y = -x + 1
We repeat same for HK
(4,4) and (-4,-2)
m = (-2-4)/(-4-4) = -6/-8 = 3/4
so we have;
y = 3x/4 + b
use (4,4) to get b
4 = 3/4(4) + b
4 = 3 + b
b = 1
so we have the equate;
y = 3x/4 + 1
multiply through by 4
4y = 3x + 4
To get the point of intersection, we have to solve the equations of the diagonals simultaneously
the equations are;
4y = 3x + 4
y = -x + 1
Multiply equation ii by 4 and i by 1
4y = 3x + 4
4y = -4x + 4
Subtract ii from i
0 = 7x
x = 0
To get y, use any of the equations;
y = -x + 1
y = 0 + 1
y = 1
So the point of intersection of both diagonals are;
(0,1)