Question

(04.04 LC)

On a coordinate grid, point T is at (2,-4) and point S is at (2,6). The distance (in units) between points T and S is
numbers, such as 2.)

Answer 1

The distance between T and S is 10 units.

Explanation:

Given the points

• T(2, -4)

• S(2, 6)

`\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad √(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

The distance between T and S is:

`=√(\left(2-2\right)^2+\left(6-\left(-4\right)\right)^2)`

`=√(\left(2-2\right)^2+\left(6+4\right)^2)`

`=√(0+10^2)`

`=√(10^2)`

`=10` ∵
`\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0`

Therefore, the distance between T and S is 10 units.