Answer:
B. 4
Step-by-step explanation:
Let x be the scale factor of the given dilation.
We have been given that the perimeter of a rectangle changes from 2.5 to 10 after a dilation. We are asked to find the scale factor of dilation.
The scale factor multiplied by the original side gives the length of new side after dilation, so we can set an equation as:
Upon substituting our given values in above equation we will get,
Upon dividing both sides of our equation by 2.5 we will get,
Therefore, the scale factor of the given dilation is 4 and option B is the correct choice.
Given:
Consider the given equation is:
To find:
The slope of the line that is represented by the given equation.
Solution:
The slope intercept form of a line is:
...(i)
Where, m is the slope and b is y-intercept.
We have,
...(ii)
On comparing (i) and (ii), we get
Therefore, the slope of the given equation is .
Answer:
Step-by-step explanation:
The image of a triangle after it has been dilated with a center at the origin has vertices at A’(-12,6) B’(6,-18) and C’ .
Point A has coordinates of (-18,9) and the pre- image of C' point C has coordinates of (18,12).
Clearly when we compare point A and point A' we see that the transformation is a dilation.
let the scale factor of dilation is 'k'.
i.e. A→ A'
i.e. k(-18,9)=(-12,6)
(-18k,9k)=(-12,6)
i.e. -18k=-12
and 9k=6
Hence, on solving we get:
k=2/3
i.e. the scale factor is 2/3.
Also,
we find the coordinates of B(c,d) by:
2/3(c,d)=(6,-18) since B→ B'
2/3×c=6
Hence c=9
and 2/3 ×d=-18
d=-27.
Hence, the coordinates of B are (9,-27).
Also the coordinates of C are (18,12)
Hence, coordinates of C' are:
Hence, the coordinates of C' are : (12,18)