Question

denisha graphed point g on the coordinate grid. she will graph point h at a location 5 units away from point g. which ordered pair could represent point h? a (-4,5) b (-9,8) c (1,3) d (-4,-1)

Explanation:

Step1: Determine the coordinates of point G

From the graph, point G has coordinates \((-3, 2)\).

Step2: Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

For option A: \(x_1=-3,y_1 = 2,x_2=-4,y_2 = 5\)
\(d=\sqrt{(-4+ 3)^2+(5 - 2)^2}=\sqrt{(-1)^2+3^2}=\sqrt{1 + 9}=\sqrt{10}
eq5\)
For option B: \(x_1=-3,y_1 = 2,x_2=-9,y_2 = 8\)
\(d=\sqrt{(-9 + 3)^2+(8 - 2)^2}=\sqrt{(-6)^2+6^2}=\sqrt{36+36}=\sqrt{72}
eq5\)
For option C: \(x_1=-3,y_1 = 2,x_2=1,y_2 = 3\)
\(d=\sqrt{(1+3)^2+(3 - 2)^2}=\sqrt{4^2+1^2}=\sqrt{16 + 1}=\sqrt{17}
eq5\)
For option D: \(x_1=-3,y_1 = 2,x_2=-4,y_2=-1\)
\(d=\sqrt{(-4 + 3)^2+(-1 - 2)^2}=\sqrt{(-1)^2+(-3)^2}=\sqrt{1+9}=5\)

Answer:

D. \((-4,-1)\)