Question

find the distance between each pair of points.
5.
6.

1. $k(2, 3), f(4, 4)$
2. $c(-3, -1), q(-2, 3)$
3. $y(2, 0), p(2, 6)$
4. $w(-2, 2), r(5, 2)$
5. $a(-7, -3), b(5, 2)$
6. $c(-3, 1), q(2, 6)$

Explanation:

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. For vertical/horizontal points, we can also use direct difference of coordinates.

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Problem 5: $F(-3,-2)$, $G(1,1)$

Step1: Identify coordinates

$x_1=-3,y_1=-2; x_2=1,y_2=1$

Step2: Apply distance formula

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

Step3: Calculate final value

$\sqrt{16+9}=\sqrt{25}=5$

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Problem 6: $D(-2,-4)$, $S(4,2)$

Step1: Identify coordinates

$x_1=-2,y_1=-4; x_2=4,y_2=2$

Step2: Apply distance formula

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

Step3: Calculate final value

$\sqrt{36+36}=\sqrt{72}=6\sqrt{2}$

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Problem 7: $K(2,3)$, $F(4,4)$

Step1: Identify coordinates

$x_1=2,y_1=3; x_2=4,y_2=4$

Step2: Apply distance formula

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

Step3: Calculate final value

$\sqrt{4+1}=\sqrt{5}$

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Problem 8: $C(-3,-1)$, $Q(-2,3)$

Step1: Identify coordinates

$x_1=-3,y_1=-1; x_2=-2,y_2=3$

Step2: Apply distance formula

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

Step3: Calculate final value

$\sqrt{1+16}=\sqrt{17}$

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Problem 9: $Y(2,0)$, $P(2,6)$

Step1: Note vertical alignment (same x)

$d=|y_2-y_1|$

Step2: Compute vertical difference

$|6-0|=6$

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Problem 10: $W(-2,2)$, $R(5,2)$

Step1: Note horizontal alignment (same y)

$d=|x_2-x_1|$

Step2: Compute horizontal difference

$|5-(-2)|=7$

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Problem 11: $A(-7,-3)$, $B(5,2)$

Step1: Identify coordinates

$x_1=-7,y_1=-3; x_2=5,y_2=2$

Step2: Apply distance formula

$d=\sqrt{(5-(-7))^2+(2-(-3))^2}=\sqrt{12^2+5^2}$

Step3: Calculate final value

$\sqrt{144+25}=\sqrt{169}=13$

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Problem 12: $C(-3,1)$, $Q(2,6)$

Step1: Identify coordinates

$x_1=-3,y_1=1; x_2=2,y_2=6$

Step2: Apply distance formula

$d=\sqrt{(2-(-3))^2+(6-1)^2}=\sqrt{5^2+5^2}$

Step3: Calculate final value

$\sqrt{25+25}=\sqrt{50}=5\sqrt{2}$

Answer:

1. $5$
2. $6\sqrt{2}$
3. $\sqrt{5}$
4. $\sqrt{17}$
5. $6$
6. $7$
7. $13$
8. $5\sqrt{2}$