Question

find the distance between each pair of points.
5.

1. l(-7,0), y(5,9)
2. u(1,3), b(4,6)
3. v(-2,5), m(0,-4)
4. c(-2,-1), k(8,3)

6.

Explanation:

Step1: Identify coordinates

For problem 5, assume \( W(x_1,y_1)\) and \( Z(x_2,y_2)\). From the graph, if \( W(-2,4)\) and \( Z(4,-2)\) (assuming standard grid - based coordinate reading).
Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute \(x_1=-2,y_1 = 4,x_2 = 4,y_2=-2\) into the formula:

$$d=\sqrt{(4-(-2))^2+(-2 - 4)^2}$$

$$=\sqrt{(4 + 2)^2+(-6)^2}$$

$$=\sqrt{6^2+(-6)^2}$$

$$=\sqrt{36+36}$$

$$=\sqrt{72}$$

$$=6\sqrt{2}\approx8.49$$

For problem 6, assume \(E(x_1,y_1)\) and \(S(x_2,y_2)\). From the graph, if \(E(-4,2)\) and \(S(4,-4)\) (assuming standard grid - based coordinate reading).
Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute \(x_1=-4,y_1 = 2,x_2 = 4,y_2=-4\) into the formula:

$$d=\sqrt{(4-(-4))^2+(-4 - 2)^2}$$

$$=\sqrt{(4 + 4)^2+(-6)^2}$$

$$=\sqrt{8^2+(-6)^2}$$

$$=\sqrt{64 + 36}$$

$$=\sqrt{100}$$

$$=10$$

For problem 7, given \(L(-7,0)\) and \(Y(5,9)\)
Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute \(x_1=-7,y_1 = 0,x_2 = 5,y_2=9\)

$$d=\sqrt{(5-(-7))^2+(9 - 0)^2}$$

$$=\sqrt{(5 + 7)^2+9^2}$$

$$=\sqrt{12^2+81}$$

$$=\sqrt{144 + 81}$$

$$=\sqrt{225}$$

$$=15$$

For problem 8, given \(U(1,3)\) and \(B(4,6)\)
Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute \(x_1=1,y_1 = 3,x_2 = 4,y_2=6\)

$$d=\sqrt{(4 - 1)^2+(6 - 3)^2}$$

$$=\sqrt{3^2+3^2}$$

$$=\sqrt{9+9}$$

$$=\sqrt{18}$$

$$=3\sqrt{2}\approx4.24$$

For problem 9, given \(V(-2,5)\) and \(M(0,-4)\)
Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute \(x_1=-2,y_1 = 5,x_2 = 0,y_2=-4\)

$$d=\sqrt{(0-(-2))^2+(-4 - 5)^2}$$

$$=\sqrt{(0 + 2)^2+(-9)^2}$$

$$=\sqrt{4+81}$$

$$=\sqrt{85}\approx9.22$$

For problem 10, given \(C(-2,-1)\) and \(K(8,3)\)
Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute \(x_1=-2,y_1=-1,x_2 = 8,y_2=3\)

$$d=\sqrt{(8-(-2))^2+(3-(-1))^2}$$

$$=\sqrt{(8 + 2)^2+(3 + 1)^2}$$

$$=\sqrt{10^2+4^2}$$

$$=\sqrt{100 + 16}$$

$$=\sqrt{116}$$

$$=2\sqrt{29}\approx10.77$$

Answer:

1. \(6\sqrt{2}\approx8.49\)
2. \(10\)
3. \(15\)
4. \(3\sqrt{2}\approx4.24\)
5. \(\sqrt{85}\approx9.22\)
6. \(2\sqrt{29}\approx10.77\)