Coordinate geometry › Points, distance and midpoints

Centroid and orthocentre coordinates

Solve the first problem 9 problems

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1. Longest side of a triangle ●○○○○ 10 ptsA triangle has vertices at coordinates $(2,2)$, $(5,6)$ and $(6,2)$. What is the length, in units, of the longest side of the triangle?
2. Shortest side of a triangle ●○○○○ 10 ptsA triangle has vertices at coordinates $(1, 2)$, $(7, 10)$ and $(1, 12)$. What is the length of the shortest side of the triangle? Round to two decimal places.
3. Centroid of a triangle ●○○○○ 10 ptsFind the centroid of the triangle with vertices $A(4, 5)$, $B(20, 25)$ and $C(30, 6)$. Give the $x$- and $y$-coordinates of the centroid.
4. Incenter of a triangle from coordinates ●●○○○ 20 ptsFind the coordinates $(x, y)$ of the incenter of the triangle with vertices $A(20, 15)$, $B(0, 0)$ and $C(-36, 15)$.
5. Orthocentre of a triangle ●●○○○ 20 ptsFind the coordinates of the orthocentre of the triangle with vertices $A(5,6)$, $B(2,4)$ and $C(1,-3)$. Round each coordinate to two decimal places.
6. Medians of a triangle in space ●●○○○ 20 ptsTriangle $ABC$ has vertices $A(0, 0, 6)$, $B(0, 4, 0)$ and $C(6, 0, 0)$. Find the lengths of the three medians of the triangle. Give each length rounded to two decimal places, listed in increasing order.
7. Centroid distance to a plane ●●●○○ 50 ptsThe vertices $A$, $B$, $C$ of an equilateral triangle $ABC$ with side length $6$ are at distances $1$, $2$ and $3$ from a plane $\alpha$. Find all possible distances from the centroid $G$ of triangle $ABC$ to the plane $\alpha$. Round each value to two decimal places and give them in increasing order.

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