Question

line segment pr is graphed below. if pr is one side of parallelogram prst, which coordinate pairs could represent vertices s and t? (6,0) and (4,1) (7,2) and (5,11) (9,2) and (6,10) (10,11) and (7,9)

Explanation:

Step1: Calculate the vector of \(PR\)

The coordinates of \(P(-7,4)\) and \(R(-4,-4)\). The vector \(\overrightarrow{PR}=(x_{R}-x_{P},y_{R}-y_{P})\).

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Step2: Check each option

• Option1: For \(S(0,0)\) and \(T(4,1)\), \(\overrightarrow{ST}=(4 - 0,1 - 0)=(4,1)

eq(3,-8)\)

• Option2: For \(S(7,3)\) and \(T(5,11)\), \(\overrightarrow{ST}=(5 - 7,11 - 3)=(-2,8)

eq(3,-8)\)

• Option3: For \(S(9,2)\) and \(T(6,10)\), \(\overrightarrow{ST}=(6 - 9,10 - 2)=(-3,8)

eq(3,-8)\)

• Option4: For \(S(10,11)\) and \(T(7,3)\), \(\overrightarrow{ST}=(7 - 10,3 - 11)=(-3,-8)\). Also, \(\overrightarrow{PS}=(10-(-7),11 - 4)=(17,7)\) and \(\overrightarrow{RT}=(7-(-4),3-(-4))=(11,7)\). In a parallelogram \(PRST\), \(\overrightarrow{PR}=\overrightarrow{ST}\) (opposite sides are parallel and equal in vector form) and \(\overrightarrow{PS}=\overrightarrow{RT}\)

Answer:

\((10,11)\) and \((7,3)\)