Question

1. triangle lmn with vertices ( l(2,-8) ), ( m(12,8) ), and ( n(14,-4) ) : ( k = \frac{1}{2} )

Explanation:

Step1: Dilate point L(2, -8) by k = 1/2

To dilate a point \((x, y)\) by a scale factor \(k\), we use the formula \((kx, ky)\). For \(L(2, -8)\) and \(k = \frac{1}{2}\):
\(x' = 2\times\frac{1}{2} = 1\)
\(y' = -8\times\frac{1}{2} = -4\)
So \(L'\) is \((1, -4)\).

Step2: Dilate point M(12, 8) by k = 1/2

Using the same dilation formula \((kx, ky)\) for \(M(12, 8)\) and \(k = \frac{1}{2}\):
\(x' = 12\times\frac{1}{2} = 6\)
\(y' = 8\times\frac{1}{2} = 4\)
So \(M'\) is \((6, 4)\).

Step3: Dilate point N(14, -4) by k = 1/2

For \(N(14, -4)\) and \(k = \frac{1}{2}\) using \((kx, ky)\):
\(x' = 14\times\frac{1}{2} = 7\)
\(y' = -4\times\frac{1}{2} = -2\)
So \(N'\) is \((7, -2)\).

Answer:

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