Search problems

7 problems match “distance formula”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

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. Area of a square from two adjacent vertices ●○○○○ 10 ptsOn a Cartesian coordinate plane, points $(2,1)$ and $(3,4)$ are adjacent vertices of a square. What is the area of the square?
3. 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.
4. Area of a square from vertices ●○○○○ 10 ptsWhat is the area, in square units, of the square with the four vertices at $A\ (0, 0)$, $B\ (-5, -1)$, $C\ (-4, -6)$ and $D\ (1, -5)$?
5. Center of a circle through three points ●●○○○ 20 ptsA circle passes through the points $(-1, 2)$, $(3,0)$ and $(9,0)$. The center of the circle is at $(h,k)$. Find the value of $h+k$.
6. 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 $C(-36, 15)$.
7. Smallest integer-centred sphere through three points ●●●○○ 50 ptsA sphere has its center at a point with integer coordinates and passes through the three points $(2,0,0)$, $(0,4,0)$, $(0,0,6)$, but does not pass through the origin $(0,0,0)$. Let $r$ be the smallest possible radius of such a sphere. Compute $r^{2}$.