Question

What is the distance between each pair points
(-1/4,-1/7) and (3/4,6/7)

Answer 1

√2

Explanation:

To find the distance between two points, we can use the distance formula:

`\boxed{\begin{array}{l}\underline{\sf Distance \;Formula}\\\\d=√((x_2-x_1)^2+(y_2-y_1)^2)\\\\\textsf{where:}\\ \phantom{ww}\bullet\;\;d\;\textsf{is the distance between two points.} \\\phantom{ww}\bullet\;\;\textsf{$(x_1,y_1)$ and $(x_2,y_2)$ are the two points.}\\\\\end{array}}`

Substitute the given points (-1/4, -1/7) and (3/4, 6/7) into the formula and solve for d:

`d=\sqrt{\left((3)/(4)-\left(-(1)/(4)\right)\right)^2+\left((6)/(7)-\left(-(1)/(7)\right)\right)^2}`

`d=\sqrt{\left((3)/(4)+(1)/(4)\right)^2+\left((6)/(7)+(1)/(7)\right)^2}`

`d=\sqrt{\left((3+1)/(4)\right)^2+\left((6+1)/(7)\right)^2}`

`d=\sqrt{\left((4)/(4)\right)^2+\left((7)/(7)\right)^2}`

`d=√(\left(1\right)^2+\left(1\right)^2)`

`d=√(1+1)`

`d=√(2)`

Therefore, the exact distance between points (-1/4, -1/7) and (3/4, 6/7) is:

`\Large\boxed{\boxed{√(2)}}`