7. Find the slope-intercept form of the equation of the line that passes through
1 answer:
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Given:
The scale factor is and the center of dilation is at the point (4,2).
Red is original figure and green is dilated figure.
To find:
The coordinates of point C' and point A.
Solution:
Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then
According to the given information, the scale factor is and the center of dilation is at (4,2).
...(i)
Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).
Using (i), we get
Therefore, the coordinates of Point C' are C'(2,5).
We assumed that point A is A(m,n).
Using (i), we get
From the given figure it is clear that the image of point A is (8,4).
On comparing both sides, we get
And,
Therefore, the coordinates of point A are (16,8).
Answer:
14.4 miles
Step-by-step explanation:
Given that :
Distance moved North = 12 miles
Distance moved West = 8 miles
Shortest distance to reach starting point :
Let shortest distance to reach starting point = d miles
Using the relation :
Longest side of a right angled triangle:
d = sqrt(8^2 + 12^2)
d = sqrt(64 + 144)
d = sqrt(208)
d = 14.422205
d = 14.4 miles (nearest tenth of a mile)
