Question

write the ordered pairs that describe the location of the points.
point r
(□,□)
point s
(□,□)

point h is located at (3.5, -2). which two points are located at a distance of 2.5 units from point h?
point i
point j
point k
point l
point m

19
graph point g by beginning at (-6, 6).
move down a distance of 8 units and then to right a distance of 1 unit.
plot point g at this location on the graph.

20
circle the points on the graph that represent the order pairs (-7, 0) and (-2,-6\frac{1}{2}).

Explanation:

Step1: Identify Point R's coordinates

Point R is on the x-axis at $x=-5$, $y=0$. So ordered pair is $(-5, 0)$.

Step2: Identify Point S's coordinates

Point S is at $x=4$, $y=-6$. So ordered pair is $(4, -6)$.

Step3: Calculate Point G's coordinates

Start at $(-6,6)$. Move down 8: $6-8=-2$. Move right 1: $-6+1=-5$. So $G=(-5,-2)$.

Step4: Find points 2.5 from H(3.5,-2)

• Point I: $(-2,1)$. Distance: $\sqrt{(3.5+2)^2+(-2-1)^2}=\sqrt{30.25+9}\approx6.27$
• Point J: $(1,3)$. Distance: $\sqrt{(3.5-1)^2+(-2-3)^2}=\sqrt{6.25+25}\approx5.61$
• Point K: $(1,-2)$. Distance: $|3.5-1|=2.5$
• Point L: $(4,0)$. Distance: $\sqrt{(3.5-4)^2+(-2-0)^2}=\sqrt{0.25+4}\approx2.06$
• Point M: $(4,-4)$. Distance: $\sqrt{(3.5-4)^2+(-2+4)^2}=\sqrt{0.25+4}\approx2.06$

Step5: Locate (-7,0) and $(-2,-6\frac{1}{2})$

$(-7,0)$ is on x-axis at $x=-7$; $(-2,-6\frac{1}{2})$ is at $x=-2$, $y=-6.5$.

Answer:

1. Point R: $(-5, 0)$; Point S: $(4, -6)$
2. Points at 2.5 units from H: Point K
3. Point G is plotted at $(-5, -2)$
4. Circled points: the point at $(-7, 0)$ and the point at $(-2, -6\frac{1}{2})$