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Question
Find the distance between the following pair of point.
T(–3, 6), R(9, –10)
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Solution
T(–3, 6), R(9, –10)
Let T (x1, y1) and R (x2, y2) be the given points.
∴ x1 = −3, y1 = 6, x2 = 9, y2 = −10
\[\mathrm{d(T,R)}=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\]
= \[\sqrt{\left[9-(-3)\right]^{2}+\left(-10-6\right)^{2}}\]
= \[\sqrt{\left(9+3\right)^{2}+\left(-10-6\right)^{2}}\]
= \[\sqrt{12^{2}+\left(-16\right)^{2}}\]
= \[\sqrt{144 + 256}\]
= \[\sqrt{400}\]
= 20
∴ d(T, R) = 20 units
∴ The distance between the points T and R 20 units.
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Case Study -2
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Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -
- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
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