Question

ge under a dilation with the given scale
r of dilation. give the coordinates of the
triangle lmn with vertices l(2, -8), m(12, 8),
and n(14, -4): k = ½
l(__,__)
m(__,__)
n(__,__)
hombus wxyz with vertices w(2, -4), x(6, -2),
(10, -4), and z(6, -6): k = 3/2

Explanation:

Step1: Recall the dilation formula

If a point \((x,y)\) is dilated with a scale factor \(k\) centered at the origin, the new point \((x',y')\) is given by \(x' = kx\) and \(y'=ky\).

Step2: Find the coordinates of \(L'\)

For \(L(2,-8)\) and \(k = \frac{1}{2}\),
\(x'=\frac{1}{2}\times2 = 1\), \(y'=\frac{1}{2}\times(-8)=-4\).

Step3: Find the coordinates of \(M'\)

For \(M(12,8)\) and \(k=\frac{1}{2}\),
\(x'=\frac{1}{2}\times12 = 6\), \(y'=\frac{1}{2}\times8 = 4\).

Step4: Find the coordinates of \(N'\)

For \(N(14,-4)\) and \(k=\frac{1}{2}\),
\(x'=\frac{1}{2}\times14=7\), \(y'=\frac{1}{2}\times(-4)=-2\).

Answer:

\(L'(1,-4)\), \(M'(6,4)\), \(N'(7,-2)\)