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:
![d(A,B) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}](https://tex.z-dn.net/?f=d%28A%2CB%29%20%3D%20%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%7D)
Putting values: x₁ = 5, x₂=5 and y₁= 4 and y₂= -2
![d(A,B) = \sqrt{(5-5)^2+(-2-4)^2}](https://tex.z-dn.net/?f=d%28A%2CB%29%20%3D%20%5Csqrt%7B%285-5%29%5E2%2B%28-2-4%29%5E2%7D)
![d(A,B) = \sqrt{(0)^2+(-6)^2}](https://tex.z-dn.net/?f=d%28A%2CB%29%20%3D%20%5Csqrt%7B%280%29%5E2%2B%28-6%29%5E2%7D)
![d(A,B) = \sqrt{36}](https://tex.z-dn.net/?f=d%28A%2CB%29%20%3D%20%5Csqrt%7B36%7D)
![d(A,B) = 6](https://tex.z-dn.net/?f=d%28A%2CB%29%20%3D%206)
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:
![d(E,F) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}](https://tex.z-dn.net/?f=d%28E%2CF%29%20%3D%20%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%7D)
Putting values: x₁ = -2, x₂=-2 and y₁= -1 and y₂= -5
![d(E,F) = \sqrt{(-2-(-2))^2+(-5-(-1))^2}](https://tex.z-dn.net/?f=d%28E%2CF%29%20%3D%20%5Csqrt%7B%28-2-%28-2%29%29%5E2%2B%28-5-%28-1%29%29%5E2%7D)
![d(E,F) = \sqrt{(0)^2+(-4)^2}](https://tex.z-dn.net/?f=d%28E%2CF%29%20%3D%20%5Csqrt%7B%280%29%5E2%2B%28-4%29%5E2%7D)
![d(E,F) = \sqrt{16}](https://tex.z-dn.net/?f=d%28E%2CF%29%20%3D%20%5Csqrt%7B16%7D)
![d(E,F) = 4](https://tex.z-dn.net/?f=d%28E%2CF%29%20%3D%204)
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:
![d(C,D) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}](https://tex.z-dn.net/?f=d%28C%2CD%29%20%3D%20%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%7D)
Putting values: x₁ = -4, x₂=1 and y₁= 1 and y₂= 1
![d(C,D)= \sqrt{(1-(-4))^2+(1-(1))^2}](https://tex.z-dn.net/?f=d%28C%2CD%29%3D%20%5Csqrt%7B%281-%28-4%29%29%5E2%2B%281-%281%29%29%5E2%7D)
![d(C,D) = \sqrt{(5)^2+(0)^2}](https://tex.z-dn.net/?f=d%28C%2CD%29%20%3D%20%5Csqrt%7B%285%29%5E2%2B%280%29%5E2%7D)
![d(C,D) = \sqrt{25}](https://tex.z-dn.net/?f=d%28C%2CD%29%20%3D%20%5Csqrt%7B25%7D)
![d(C,D) = 5](https://tex.z-dn.net/?f=d%28C%2CD%29%20%3D%205)
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:
![d(G,H) = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}](https://tex.z-dn.net/?f=d%28G%2CH%29%20%3D%20%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E2%2B%28y_%7B2%7D-y_%7B1%7D%29%5E2%7D)
Putting values: x₁ = 3, x₂=6 and y₁= -5 and y₂= -5
![d(G,H)= \sqrt{(6-(3))^2+(-5-(-5))^2}](https://tex.z-dn.net/?f=d%28G%2CH%29%3D%20%5Csqrt%7B%286-%283%29%29%5E2%2B%28-5-%28-5%29%29%5E2%7D)
![d(G,H) = \sqrt{(3)^2+(0)^2}](https://tex.z-dn.net/?f=d%28G%2CH%29%20%3D%20%5Csqrt%7B%283%29%5E2%2B%280%29%5E2%7D)
![d(G,H) = \sqrt{9}](https://tex.z-dn.net/?f=d%28G%2CH%29%20%3D%20%5Csqrt%7B9%7D)
![d(G,H) = 3](https://tex.z-dn.net/?f=d%28G%2CH%29%20%3D%203)
Distance between points G(3, -5) and H(6, -5) is 3 units