Let's solve the problem step by step using the
Pythagorean distance formula:
$$
d(x, y) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$
We will calculate the distance between each pair of points on the coordinate grid to the
nearest hundredth.
---
Step 1: Identify coordinates of each point from the graph
From the image, we read off the coordinates of each labeled point:
-
A: (8, 3)
-
B: (0, -6)
-
C: (-5, 8)
-
D: (-1, 4)
-
E: (-2, 0)
-
F: (-9, -7)
-
G: (0, -3)
-
H: (0, -9)
-
J: (2, -4)
-
K: (0, 1)
-
M: (-4, -5)
-
N: (-3, -8)
-
P: (2, 9)
-
Q: (-5, 7)
-
R: (4, 2)
-
S: (-5, 0)
-
T: (8, -9)
-
V: (6, -3)
-
W: (-3, -7)
-
Z: (1, 0)
---
Now compute each distance:
---
1. $ d(A, B) $
A(8, 3), B(0, -6)
$$
d = \sqrt{(0 - 8)^2 + (-6 - 3)^2} = \sqrt{(-8)^2 + (-9)^2} = \sqrt{64 + 81} = \sqrt{145} \approx 12.04
$$
✔ 12.04
---
2. $ d(E, F) $
E(-2, 0), F(-9, -7)
$$
d = \sqrt{(-9 + 2)^2 + (-7 - 0)^2} = \sqrt{(-7)^2 + (-7)^2} = \sqrt{49 + 49} = \sqrt{98} \approx 9.90
$$
✔ 9.90
---
3. $ d(J, K) $
J(2, -4), K(0, 1)
$$
d = \sqrt{(0 - 2)^2 + (1 + 4)^2} = \sqrt{(-2)^2 + (5)^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.39
$$
✔ 5.39
---
4. $ d(P, Q) $
P(2, 9), Q(-5, 7)
$$
d = \sqrt{(-5 - 2)^2 + (7 - 9)^2} = \sqrt{(-7)^2 + (-2)^2} = \sqrt{49 + 4} = \sqrt{53} \approx 7.28
$$
✔ 7.28
---
5. $ d(T, V) $
T(8, -9), V(6, -3)
$$
d = \sqrt{(6 - 8)^2 + (-3 + 9)^2} = \sqrt{(-2)^2 + (6)^2} = \sqrt{4 + 36} = \sqrt{40} \approx 6.32
$$
✔ 6.32
---
6. $ d(C, D) $
C(-5, 8), D(-1, 4)
$$
d = \sqrt{(-1 + 5)^2 + (4 - 8)^2} = \sqrt{(4)^2 + (-4)^2} = \sqrt{16 + 16} = \sqrt{32} \approx 5.66
$$
✔ 5.66
---
7. $ d(G, H) $
G(0, -3), H(0, -9)
$$
d = \sqrt{(0 - 0)^2 + (-9 + 3)^2} = \sqrt{0 + (-6)^2} = \sqrt{36} = 6.00
$$
✔ 6.00
---
8. $ d(M, N) $
M(-4, -5), N(-3, -8)
$$
d = \sqrt{(-3 + 4)^2 + (-8 + 5)^2} = \sqrt{(1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.16
$$
✔ 3.16
---
9. $ d(R, S) $
R(4, 2), S(-5, 0)
$$
d = \sqrt{(-5 - 4)^2 + (0 - 2)^2} = \sqrt{(-9)^2 + (-2)^2} = \sqrt{81 + 4} = \sqrt{85} \approx 9.22
$$
✔ 9.22
---
10. $ d(W, Z) $
W(-3, -7), Z(1, 0)
$$
d = \sqrt{(1 + 3)^2 + (0 + 7)^2} = \sqrt{(4)^2 + (7)^2} = \sqrt{16 + 49} = \sqrt{65} \approx 8.06
$$
✔ 8.06
---
Final Answers:
$$
\begin{align*}
d(A,B) &= 12.04 \\
d(E,F) &= 9.90 \\
d(J,K) &= 5.39 \\
d(P,Q) &= 7.28 \\
d(T,V) &= 6.32 \\
d(C,D) &= 5.66 \\
d(G,H) &= 6.00 \\
d(M,N) &= 3.16 \\
d(R,S) &= 9.22 \\
d(W,Z) &= 8.06 \\
\end{align*}
$$
---
✔ All distances are rounded to the
nearest hundredth as requested.
Let me know if you'd like this in a printable format or with visual explanation!
Parent Tip: Review the logic above to help your child master the concept of distance between two points worksheet.
