Find the distance between each of the following pairs of points. T(-3, 6), R(9, -10)
T(–3, 6), R(9, –10)
\[TR = \sqrt{\left( – 3 – 9 \right)^2 + \left( 6 – \left( – 10 \right) \right)^2} = \sqrt{\left( – 12 \right)^2 + \left( 16 \right)^2}\]
\[ = \sqrt{144 + 256} = \sqrt{400}\]
\[ = 20\]
Explanation:-
The above calculation is finding the distance between two points, T and R, which are given as (-3, 6) and (9, -10) respectively. The formula used here is the distance formula, which is used to find the distance between two points in a coordinate plane.
The distance formula is given as: distance = sqrt((x2-x1)^2 + (y2-y1)^2)
Here, (x1, y1) = (-3, 6) and (x2, y2) = (9, -10). Substituting these values in the formula, we get:
TR = sqrt((9 – (-3))^2 + (-10 – 6)^2) = sqrt((9 + 3)^2 + (-16)^2) = sqrt(12^2 + 16^2) = sqrt(144 + 256) = sqrt(400) = 20
Therefore, the distance between points T and R is 20 units.