Answer:
Slope of line M'N' is 1.
Step-by-step explanation:
Given: M= (2,4) and N = (3, 5) ; K = 0.8
The rule of dilation with origin as the center:
\((x ,y) \rightarrow (kx , ky)\) where k is the scale factor i.e k = 0.8
or \((x ,y) \rightarrow (0.8x , 0.8y)\)
Then:
Apply this on coordinates of MNOPQ to find M' and N'.
\(M(2 ,4) \times (0.8\cdot 2 , 0.8\cdot 4)\) = M'(1.6 , 3.2)
\(N(3 ,5) \times (0.8\cdot 3 , 0.8\cdot 5)\) = N'(2.4 , 4)
Slope of line for any two points \((x_1 , y_1)\) and \((x_2, y_2)\) is given by:
\(m = \frac{y_2-y_1}{x_2-x_1}\)
To find the slope of line M'N':
we have M' = (1.6 , 3.2) and N' = (2.4, 4)
then by slope formula;
Slope of line M'N' = \(\frac{4-3.2}{2.4-1.6}=\frac{0.8}{0.8} = 1\)
Therefore, slope of line M'N' is 1.
