Jawaban:

Jawab:

a. \begin{gathered} CD = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}} \\ = \sqrt{(5 - (-3))^{2} + (-6 - 9)^{2}} \\ = \sqrt{(5 + 3)^{2} + (-6 - 9)^{2}} \\ = \sqrt{8^{2} + (-15)^{2}} \\ = \sqrt{64 + 225} \\ = \sqrt{289} \\ = 17 \end{gathered}

CD=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

=

(5−(−3))

2

+(−6−9)

2

=

(5+3)

2

+(−6−9)

2

=

8

2

+(−15)

2

=

64+225

=

289

=17

b. \begin{gathered} PQ = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}} \\ = \sqrt{(-9 - 7)^{2} + (8 - (-4))^{2}} \\ = \sqrt{(-9 - 7)^{2} + (8 + 4)^{2}} \\ = \sqrt{(-16)^{2} + 12^{2}} \\ = \sqrt{256 + 144} \\ = \sqrt{400} \\ = 20 \end{gathered}

PQ=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

=

(−9−7)

2

+(8−(−4))

2

=

(−9−7)

2

+(8+4)

2

=

(−16)

2

+12

2

=

256+144

=

400

=20

c, \begin{gathered} KL = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}} \\ = \sqrt{(-11 - (-5))^{2} + (-8 - (-12))^{2}} \\ = \sqrt{(-11 + 5)^{2} + (-8 + 12)^{2}} \\ = \sqrt{(-6)^{2} + 4^{2}} \\ = \sqrt{36 + 16} \\ = \sqrt{52} \\ = 2 \sqrt{13} \end{gathered}

KL=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

=

(−11−(−5))

2

+(−8−(−12))

2

=

(−11+5)

2

+(−8+12)

2

=

(−6)

2

+4

2

=

36+16

=

52

=2

13

Jadi, panjang garis CD, PQ, dan KL berturut-turut adalah 17, 20, dan 2 \sqrt{13}2

13

.