Question

ex. 4
find the coordinates of the vertices when dilated by a scale factor of 2.5 about the origin.
f (0, -1), c (0, 1), h (1, 1)
f
c
h
algebraic description:

Explanation:

Step1: Recall the dilation formula

When a point \((x,y)\) is dilated about the origin with a scale factor \(k\), the new coordinates \((x',y')\) are given by \((x',y')=(kx,ky)\). Here \(k = 2.5\).

Step2: Calculate \(F'\)

For point \(F(0,-1)\), using the formula \((x',y')=(kx,ky)\) with \(x = 0\), \(y=-1\) and \(k = 2.5\).
\(x'=2.5\times0 = 0\), \(y'=2.5\times(-1)=-2.5\). So \(F'=(0,-2.5)\).

Step3: Calculate \(C'\)

For point \(C(0,1)\), using the formula \((x',y')=(kx,ky)\) with \(x = 0\), \(y = 1\) and \(k = 2.5\).
\(x'=2.5\times0=0\), \(y'=2.5\times1 = 2.5\). So \(C'=(0,2.5)\).

Step4: Calculate \(H'\)

For point \(H(1,1)\), using the formula \((x',y')=(kx,ky)\) with \(x = 1\), \(y = 1\) and \(k = 2.5\).
\(x'=2.5\times1=2.5\), \(y'=2.5\times1 = 2.5\). So \(H'=(2.5,2.5)\).

Answer:

\(F'=(0,-2.5)\), \(C'=(0,2.5)\), \(H'=(2.5,2.5)\)