Question

1. quadrilateral fish has coordinates f(-8,11), i(-7,9), s (0,6), h(-2,-3) and then is translated so that h=(3,-7). find the coordinates of f, i and s.

Explanation:

Step1: Find the translation vector

Let the translation vector be \((a, b)\). For point \(H(-2, -3)\) translated to \(H'(3, -7)\), we use the translation formula \(x' = x + a\) and \(y' = y + b\).
For the \(x\)-coordinate: \(3 = -2 + a\), so \(a = 3 - (-2) = 5\).
For the \(y\)-coordinate: \(-7 = -3 + b\), so \(b = -7 - (-3) = -4\).
The translation vector is \((5, -4)\).

Step2: Translate point F

For point \(F(-8, 11)\), using the translation vector \((5, -4)\):
\(x'\) of \(F'\) is \(-8 + 5 = -3\).
\(y'\) of \(F'\) is \(11 + (-4) = 7\).
So \(F' = (-3, 7)\).

Step3: Translate point I

For point \(I(-7, 9)\), using the translation vector \((5, -4)\):
\(x'\) of \(I'\) is \(-7 + 5 = -2\).
\(y'\) of \(I'\) is \(9 + (-4) = 5\).
So \(I' = (-2, 5)\).

Step4: Translate point S

For point \(S(0, 6)\), using the translation vector \((5, -4)\):
\(x'\) of \(S'\) is \(0 + 5 = 5\).
\(y'\) of \(S'\) is \(6 + (-4) = 2\).
So \(S' = (5, 2)\).

Answer:

\(F' = (-3, 7)\), \(I' = (-2, 5)\), \(S' = (5, 2)\)