Question

1. you are given the following ordered pairs.

(3.5, -1)(-1.5, 3)(-3, 3)(3.5, 2.5)(-1.5, -1.5)
part a
graph the ordered pairs on the coordinate plane.
part b
find the two ordered pairs on the coordinate plane
that are 4.5 units apart.
104 2 - 5 find distances on the coordinate plane

Explanation:

Step1: Analyze \( (3.5,-1) \) and \( (3.5,2.5) \)

For two points \((x_1,y_1)\) and \((x_2,y_2)\), if \(x_1 = x_2\), the distance \(d=\vert y_2 - y_1\vert\).
Here \(x_1=x_2 = 3.5\), \(y_1=-1\), \(y_2 = 2.5\).
\(d=\vert2.5-(-1)\vert=\vert2.5 + 1\vert=\vert3.5\vert
eq4.5\)

Step2: Analyze \( (3.5,-1) \) and \( (-1.5,3) \)

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
\(x_1 = 3.5\), \(y_1=-1\), \(x_2=-1.5\), \(y_2 = 3\)
\(d=\sqrt{(-1.5 - 3.5)^2+(3+1)^2}=\sqrt{(-5)^2+4^2}=\sqrt{25 + 16}=\sqrt{41}
eq4.5\)

Step3: Analyze \( (3.5,-1) \) and \( (-3,3) \)

\(x_1 = 3.5\), \(y_1=-1\), \(x_2=-3\), \(y_2 = 3\)
\(d=\sqrt{(-3 - 3.5)^2+(3 + 1)^2}=\sqrt{(-6.5)^2+4^2}=\sqrt{42.25+16}=\sqrt{58.25}
eq4.5\)

Step4: Analyze \( (3.5,-1) \) and \( (-1.5,-1.5) \)

\(x_1 = 3.5\), \(y_1=-1\), \(x_2=-1.5\), \(y_2=-1.5\)
\(d=\sqrt{(-1.5 - 3.5)^2+(-1.5 + 1)^2}=\sqrt{(-5)^2+(-0.5)^2}=\sqrt{25+0.25}=\sqrt{25.25}
eq4.5\)

Step5: Analyze \( (-1.5,3) \) and \( (-3,3) \)

Since \(y_1=y_2 = 3\), \(d=\vert x_2 - x_1\vert\).
\(x_1=-1.5\), \(x_2=-3\)
\(d=\vert-3+1.5\vert=\vert-1.5\vert
eq4.5\)

Step6: Analyze \( (-1.5,3) \) and \( (3.5,2.5) \)

\(x_1=-1.5\), \(y_1 = 3\), \(x_2=3.5\), \(y_2=2.5\)
\(d=\sqrt{(3.5 + 1.5)^2+(2.5 - 3)^2}=\sqrt{5^2+(-0.5)^2}=\sqrt{25 + 0.25}=\sqrt{25.25}
eq4.5\)

Step7: Analyze \( (-1.5,3) \) and \( (-1.5,-1.5) \)

Since \(x_1=x_2=-1.5\), \(d=\vert y_2 - y_1\vert\)
\(y_1 = 3\), \(y_2=-1.5\)
\(d=\vert-1.5 - 3\vert=\vert-4.5\vert=4.5\)

Step8: Analyze \( (-3,3) \) and \( (3.5,2.5) \)

\(x_1=-3\), \(y_1 = 3\), \(x_2=3.5\), \(y_2=2.5\)
\(d=\sqrt{(3.5 + 3)^2+(2.5 - 3)^2}=\sqrt{6.5^2+(-0.5)^2}=\sqrt{42.25 + 0.25}=\sqrt{42.5}
eq4.5\)

Step9: Analyze \( (-3,3) \) and \( (-1.5,-1.5) \)

\(x_1=-3\), \(y_1 = 3\), \(x_2=-1.5\), \(y_2=-1.5\)
\(d=\sqrt{(-1.5 + 3)^2+(-1.5 - 3)^2}=\sqrt{1.5^2+(-4.5)^2}=\sqrt{2.25 + 20.25}=\sqrt{22.5}
eq4.5\)

Step10: Analyze \( (3.5,2.5) \) and \( (-1.5,-1.5) \)

\(x_1=3.5\), \(y_1 = 2.5\), \(x_2=-1.5\), \(y_2=-1.5\)
\(d=\sqrt{(-1.5 - 3.5)^2+(-1.5 - 2.5)^2}=\sqrt{(-5)^2+(-4)^2}=\sqrt{25 + 16}=\sqrt{41}
eq4.5\)

Answer:

\((-1.5,3)\) and \((-1.5,-1.5)\)