Question

13 multiple choice 1 point line segment ab is graphed below. if ab is one side of parallelogram abcd, which coordinate pairs could present vertices c and d? (-1,6) and (1,0) (4,2) and (4,-4) (-1,5) and (2,-1) (-2,3) and (-1,-2)

Explanation:

Step1: Find the vector of \(AB\)

Let \(A(-5,2)\) and \(B(-2,-4)\). The vector \(\overrightarrow{AB}=(x_{B}-x_{A},y_{B}-y_{A})=(-2 - (-5),-4 - 2)=(3,-6)\)

Step2: Check each option

• Option 1:

Let \(C(-1,6)\) and \(D(1,0)\). The vector \(\overrightarrow{CD}=(1-(-1),0 - 6)=(2,-6)
eq(3,-6)\)

• Option 2:

Let \(C(4,2)\) and \(D(4,-4)\). The vector \(\overrightarrow{CD}=(4 - 4,-4 - 2)=(0,-6)
eq(3,-6)\)

• Option 3:

Let \(C(-1,5)\) and \(D(2,-1)\). The vector \(\overrightarrow{CD}=(2-(-1),-1 - 5)=(3,-6)\)

• Option 4:

Let \(C(-2,3)\) and \(D(-1,-2)\). The vector \(\overrightarrow{CD}=(-1-(-2),-2 - 3)=(1,-5)
eq(3,-6)\)

Answer:

\((-1,5)\) and \((2,-1)\)