Answer:
a) Distance between points A (5, 4) and B( 5, -2) is 6 units
b) Distance between points E (-2, -1) and F( -2, -5) is 4 units
c) Distance between points C (-4, 1) and D( 1, 1) is 5 units
d) Distance between points G(3, -5) and H(6, -5) is 3 units
Step-by-step explanation:
We need to find the distance between each pair
a) A (5, 4) and B( 5, -2)
the distance formula is:
[tex]d(A,B) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Putting values: x₁ = 5, x₂=5 and y₁= 4 and y₂= -2
[tex]d(A,B) = \sqrt{(5-5)^2+(-2-4)^2}[/tex]
[tex]d(A,B) = \sqrt{(0)^2+(-6)^2}[/tex]
[tex]d(A,B) = \sqrt{36}[/tex]
[tex]d(A,B) = 6[/tex]
Distance between points A (5, 4) and B( 5, -2) is 6 units
b) E (-2, -1) and F( -2, -5)
the distance formula is:
[tex]d(E,F) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Putting values: x₁ = -2, x₂=-2 and y₁= -1 and y₂= -5
[tex]d(E,F) = \sqrt{(-2-(-2))^2+(-5-(-1))^2}[/tex]
[tex]d(E,F) = \sqrt{(0)^2+(-4)^2}[/tex]
[tex]d(E,F) = \sqrt{16}[/tex]
[tex]d(E,F) = 4[/tex]
Distance between points E (-2, -1) and F( -2, -5) is 4 units
c) C (-4, 1) and D( 1, 1)
the distance formula is:
[tex]d(C,D) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Putting values: x₁ = -4, x₂=1 and y₁= 1 and y₂= 1
[tex]d(C,D)= \sqrt{(1-(-4))^2+(1-(1))^2}[/tex]
[tex]d(C,D) = \sqrt{(5)^2+(0)^2}[/tex]
[tex]d(C,D) = \sqrt{25}[/tex]
[tex]d(C,D) = 5[/tex]
Distance between points C (-4, 1) and D( 1, 1) is 5 units
d) G(3, -5) and H(6, -5)
the distance formula is:
[tex]d(G,H) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Putting values: x₁ = 3, x₂=6 and y₁= -5 and y₂= -5
[tex]d(G,H)= \sqrt{(6-(3))^2+(-5-(-5))^2}[/tex]
[tex]d(G,H) = \sqrt{(3)^2+(0)^2}[/tex]
[tex]d(G,H) = \sqrt{9}[/tex]
[tex]d(G,H) = 3[/tex]
Distance between points G(3, -5) and H(6, -5) is 3 units
