Question

question 1 (39 points)
what are the coordinates for
j = (, ) k = (, ) l = (, )
j = (, ) k = (, ) l = (, )
each one is multiplied by what to get the scale factor of (you can use fraction or decimal)
word bank:
4 14 3 6 6.5 1/2 2 2 7 3 6 0.5 12 4

Explanation:

Step1: Find coordinates of \(J\), \(K\), \(L\)

For a point \((x,y)\) on the coordinate - plane, \(x\) is the horizontal (abscissa) and \(y\) is the vertical (ordinate) value.
For point \(J\): \(x = 5\), \(y = 6\), so \(J=(5,6)\)
For point \(K\): \(x = 13\), \(y = 6\), so \(K=(13,6)\)
For point \(L\): \(x = 4\), \(y = 14\), so \(L=(4,14)\)

Step2: Find coordinates of \(J'\), \(K'\), \(L'\)

For point \(J'\): \(x = 2\), \(y = 3\), so \(J'=(2,3)\)
For point \(K'\): \(x = 7\), \(y = 3\), so \(K'=(7,3)\)
For point \(L'\): \(x = 2\), \(y = 7\), so \(L'=(2,7)\)

Step3: Calculate the scale factor

The scale factor \(k\) for a dilation from a point \((x,y)\) to \((x',y')\) is given by \(k=\frac{x'}{x}=\frac{y'}{y}\)
Take point \(J=(5,6)\) and \(J'=(2,3)\)
\(k=\frac{2}{5}= 0.5\) or \(\frac{1}{2}\) (using \(x\) - values: \(\frac{2}{4}=0.5\) for \(L=(4,14)\) and \(L'=(2,7)\), using \(y\) - values: \(\frac{3}{6}=0.5\) for \(J=(5,6)\) and \(J'=(2,3)\))

Answer:

\(J=(5,6)\), \(K=(13,6)\), \(L=(4,14)\), \(J'=(2,3)\), \(K'=(7,3)\), \(L'=(2,7)\), scale factor \( = 0.5\) (or \(\frac{1}{2}\))