Triangle ABC

Question

A
B
C
has vertices point A(−2,−2)
A
(
−
2
,
−
2
)
, point B(−4,−3)
B
(
−
4
,
−
3
)
, and point C(−2,−5)
C
(
−
2
,
−
5
)
. Find the coordinates of A′
A
′
, B′
B
′
, and C′
C
′
after a dilation with a scale factor of 3
3
and a center point of dilation at the origin.(2 points)

Answer 1

To find the coordinates of points A', B', and C' after a dilation with a scale factor of 3 and center point at the origin, you can use the formula for dilation:

\[ (x', y') = (k \cdot x, k \cdot y) \]

where \((x, y)\) are the original coordinates of the points, \(k\) is the scale factor, and \((x', y')\) are the new coordinates after dilation.

Given that the scale factor \(k = 3\):

1. For point A(-2, -2): \[ A' = (3 \cdot -2, 3 \cdot -2) = (-6, -6) \]

2. For point B(-4, -3): \[ B' = (3 \cdot -4, 3 \cdot -3) = (-12, -9) \]

3. For point C(-2, -5): \[ C' = (3 \cdot -2, 3 \cdot -5) = (-6, -15) \]

Thus, the coordinates after the dilation are:

• \(A'(-6, -6)\)
• \(B'(-12, -9)\)
• \(C'(-6, -15)\)