Question

Find the dilation of 0.5 with a center (0,0) for the folloing ponits a (6,7) b (-7,-1)
a=(___,___)
b=(____,___)

Answer 1

To find the dilation of points with a center at (0,0) and a scale factor of \( k = 0.5 \), we can use the formula:

\[
(x', y') = (kx, ky)
\]

where \( (x, y) \) are the original coordinates of the point, and \( (x', y') \) are the new coordinates after dilation.

For point \( a(6, 7) \):

\[
x' = 0.5 \cdot 6 = 3
\]
\[
y' = 0.5 \cdot 7 = 3.5
\]

So the dilated point \( a \) is:

\[
a = (3, 3.5)
\]

For point \( b(-7, -1) \):

\[
x' = 0.5 \cdot (-7) = -3.5
\]
\[
y' = 0.5 \cdot (-1) = -0.5
\]

So the dilated point \( b \) is:

\[
b = (-3.5, -0.5)
\]

Putting it all together:

\( a = (3, 3.5) \)

\( b = (-3.5, -0.5) \)