Question

dilate △qrs by a scale factor of 3 with the center of dilation at the origin.
point q: (-3, 9)
what are the coordinates of point r and point s?
point r: ( , ? )
point s: ( ?, ? )
(on the grid: q (-1,3), s (-3,2), r (-1,0))

Explanation:

Step1: Recall Dilation Rule

To dilate a point \((x, y)\) with center at the origin and scale factor \(k\), we use the rule \((x, y) \to (k \cdot x, k \cdot y)\). Here, the scale factor \(k = 3\).

Step2: Find Coordinates of \(R'\)

The coordinates of point \(R\) are \((-1, 0)\). Applying the dilation rule:
\(x'\) - coordinate: \(3 \times (-1) = -3\)
\(y'\) - coordinate: \(3 \times 0 = 0\)
So, \(R' = (-3, 0)\).

Step3: Find Coordinates of \(S'\)

The coordinates of point \(S\) are \((-3, 2)\). Applying the dilation rule:
\(x'\) - coordinate: \(3 \times (-3) = -9\)
\(y'\) - coordinate: \(3 \times 2 = 6\)
So, \(S' = (-9, 6)\).

Answer:

Point \(R'\): \((-3, 0)\)
Point \(S'\): \((-9, 6)\)