The image<span> is inverted. The </span>figure<span> and the </span>image<span> have a common point. The common point is the </span>center<span> of </span>dilation<span>. </span>
The first step is to find the slope. Use the slope formula
m = (y2-y1)/(x2-x1)
The two points are (x1,y1) = (-1,5) and (x2,y2) = (2,-1)
So,
x1 = -1
y1 = 5
and
x2 = 2
y2 = -1
will be plugged into the slope formula to get...
m = (y2-y1)/(x2-x1)
m = (-1-5)/(2-(-1))
m = (-1-5)/(2+1)
m = (-6)/(3)
m = -2
The slope is -2
Use m = -2 and one of the points to find the y intercept b. I'll use the point (x,y) = (-1,5) ---> x = -1, y = 5
y = mx+b ... slope intercept form
5 = -2*(-1)+b
5 = 2+b
5-2 = 2+b-2
3 = b
b = 3
The y intercept is 3
-----------------------------------
m = -2 is the slope
b = 3 is the y intercept
Therefore y = mx+b turns into y = -2x+3 as the equation that goes through the two points
- 2 because we obtain : - 2x - 2y = - 16 ;
We solve the system:
5x + 2y = 30
-2x - 2y = -16
_____________(+)
3x / = 14;
x = 14/3;
y = 8 - 14/3;
y = 24/3 -14/3;
y = 10/3;
The solution of the system is ( 14/3 ; 10/3 )
