Question

1. rhombus jklm with vertices j(-4,7), k(0,8), l(-1,4), and m(-5,3): (x,y)→(x + 2,y - 2)
2. square wxyz with vertices w(1,7), x(6,5), y(4,0), and z(-1,2): (x,y)→(x - 7,y)

a quantity with both direction and magnitude or size

• a vector is represented in the coordinate plane by an arrow drawn from an initial point p, to terminal point q.
• the vector is denoted as pq and read as \vector pq.\
• the component form of a vector is written as where a is the horizontal component and b is the vertical component.

Explanation:

Step1: Apply transformation to rhombus JKM's vertices

For point \(J(-4,7)\) with transformation \((x,y)\to(x + 2,y-2)\), we have \(x=-4,y = 7\). Then \(x'=-4 + 2=-2,y'=7-2 = 5\), so \(J'(-2,5)\).
For point \(K(0,8)\), \(x = 0,y = 8\), \(x'=0 + 2=2,y'=8-2=6\), so \(K'(2,6)\).
For point \(L(-1,4)\), \(x=-1,y = 4\), \(x'=-1+2 = 1,y'=4 - 2=2\), so \(L'(1,2)\).
For point \(M(-5,3)\), \(x=-5,y = 3\), \(x'=-5+2=-3,y'=3-2 = 1\), so \(M'(-3,1)\).

Step2: Apply transformation to square WXYZ's vertices

For point \(W(1,7)\) with transformation \((x,y)\to(x - 7,y)\), we have \(x = 1,y = 7\), \(x'=1-7=-6,y'=7\), so \(W'(-6,7)\).
For point \(X(6,5)\), \(x = 6,y = 5\), \(x'=6-7=-1,y'=5\), so \(X'(-1,5)\).
For point \(Y(4,0)\), \(x = 4,y = 0\), \(x'=4-7=-3,y'=0\), so \(Y'(-3,0)\).
For point \(Z(-1,2)\), \(x=-1,y = 2\), \(x'=-1-7=-8,y'=2\), so \(Z'(-8,2)\).

Answer:

\(J':(-2,5)\)
\(K':(2,6)\)
\(L':(1,2)\)
\(M':(-3,1)\)
\(W':(-6,7)\)
\(X':(-1,5)\)
\(Y':(-3,0)\)
\(Z':(-8,2)\)