Question

the vertices of parallelogram gram are g(-8,2), r(-7,6), a(-4,6), and m(-5,2). graph gram and gram, its image after a translation 11 units right and 2 units up. choose the correct graph below. \\(\bigcirc\\) a. \\(\bigcirc\\) b. \\(\bigcirc\\) c. \\(\bigcirc\\) d.

Explanation:

Step1: Recall translation rule

To translate a point \((x,y)\) \(h\) units right and \(k\) units up, the new coordinates are \((x + h,y + k)\). Here, \(h = 11\) and \(k=2\).

Step2: Find translated coordinates

• For \(G(-8,2)\): New \(x=-8 + 11=3\), new \(y = 2+2 = 4\), so \(G'=(3,4)\)
• For \(R(-7,6)\): New \(x=-7 + 11 = 4\), new \(y=6 + 2=8\), so \(R'=(4,8)\)
• For \(N(-4,6)\): New \(x=-4+11 = 7\), new \(y=6 + 2=8\), so \(N'=(7,8)\)
• For \(M(-5,2)\): New \(x=-5 + 11=6\), new \(y=2+2 = 4\), so \(M'=(6,4)\)

Step3: Analyze the graph

The original parallelogram has vertices with \(y\)-coordinates 2 and 6 (for \(G,M\) and \(R,N\) respectively). After translation, \(y\)-coordinates become 4 and 8. So the translated parallelogram should be above the original. Also, the \(x\)-coordinates shift from negative to positive (since we add 11 to negative \(x\)-values). Looking at the options, option A shows the translated figure with higher \(y\)-coordinates (since the original has lower \(y\) and translated has higher) and correct \(x\)-shift.

Answer:

A