Question

Match the expressions on the left which represent distance two points, with their corresponding points on the right.

Answer 1

[(3, 1), (5, 6)]

[(4, -2), (0, -8)]

[(5, 4), (2, 0)]

[(-1, -3), (-1, -7)]

Step-by-step explanation:

The distance between two points (x1, y1) and (x2, y2) can be calculated as:

`\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2_{}}`

So, if we have the expression:

`\sqrt[]{(5-3)^2+(6-1)^2}`

The coordinates of (x1, y1) are (3, 1) and the coordinates of (x2, y2) are (5, 6)

In the same way, for the other expression we get:

`\begin{gathered} \sqrt[]{(0-4)^2+(-8+2)^2}=\sqrt[]{(0-4)^2+(-8-(-2))^2} \\ \to(x_(1,)y_1)=(4,-2) \\ \to(x_(2,)y_2)=(0,-8) \end{gathered}`
`\begin{gathered} \sqrt[]{(2-5)^2+(0-4)^2} \\ \to(x_(1,)y_1)=(5,4) \\ \to(x_2,y_2)=(2,0) \end{gathered}`
`\begin{gathered} \sqrt[]{(-1+1)^2+(-7_{}+3)^2}=\sqrt[]{(-1-(-1))^2+(-7_{}-(-3))^2} \\ \to(x_1,y_1)=(-1,-3) \\ \to(x_2,y_2)=(-1,-7) \end{gathered}`

So, the answer in order are:

[(3, 1), (5, 6)]

[(4, -2), (0, -8)]

[(5, 4), (2, 0)]

[(-1, -3), (-1, -7)]