Points of concurrency Quiz 1

Question 1

A triangle with the points $$\left( 0,0 ight),\left( 4,10 ight)$$ and $$\left( 10,0 ight)$$ is constructed on a cartesian plane. A student wishes to find the point of concurrency by calculating the centroid of the triangle. Calculate the centroid of the given triangle.  $$ \ $$  <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/062347fb-c9ad-4e95-ab8d-6edeef6ec10c1205601871942498664.png"/>

Accepted Answer

$$\left( \dfrac{14}{3},\dfrac{10}{3} \right)$$

Answer

$$\left( \dfrac{14}{3},\dfrac{14}{3} \right)$$

Answer

$$\left( \dfrac{10}{3},\dfrac{10}{3} \right)$$

Answer

$$\left( \dfrac{10}{3},\dfrac{14}{3} \right)$$

Question 2

An equilateral triangle with length $$15$$ units is being constructed. A student wishes to find the point of concurrency. Given that orthocenter is the point of concurrency by dropping altitudes from each side, determine the orthocenter of the triangle. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/76a4c0f0-6883-497a-bbfd-23ab6b806f422236483425808672073.png"/>

Accepted Answer

$$O=\left( 7.5,\dfrac{13}{3} \right)$$

Answer

$$O=\left( \dfrac{13}{3},4.5 \right)$$

Answer

$$O=\left( \dfrac{13}{3},7.5 \right)$$

Answer

$$O=\left( 4.5,\dfrac{13}{3} \right)$$

Question 3

A triangle with the points $$\left( 0,0 ight),\left( 3,4 ight)$$ and $$\left( 6,0 ight)$$ is constructed on a cartesian plane. Calculate the incenter of the given triangle.$$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/b7d37147-91f6-47e5-849e-d45c01b69fde2439183406900388842.png"/>

Accepted Answer

$$IC=\left( 3,1.5 \right)$$

Answer

$$IC=\left( 1.5,1.5 \right)$$

Answer

$$IC=\left( 3,3 \right)$$

Answer

$$IC=\left( 1.5,3 \right)$$

Question 4

A triangle with points $$\left( 0,0 ight),\left( 10,0 ight)$$ and $$\left( 5,5 ight)$$ with an angle of $$90^\circ$$ has a circumcenter lying on the triangle. Given that the triangle is constructed on a cartesian plane, calculate the point of the circumcenter.$$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/8675714a-1041-4cdf-865c-b78d305d13068967934626483415100.png"/>

Accepted Answer

$$\left( 5,0 \right)$$

Answer

$$\left( 15,10 \right)$$

Answer

$$\left( 10,15 \right)$$

Answer

$$\left( 0,5 \right)$$

Question 5

A triangle has an angle of $$90^\circ$$ in the $$1	ext{st}$$ quadrant at point $$(0,0)$$. Given that the triangle follows the $$1:\sqrt{2}:1$$ special triangle rule, the length of its shortest side is $$6$$ units, calculate the circumcenter of the triangle.

Accepted Answer

$$(2,4)$$

Answer

$$(2,2)$$

Answer

$$(4,2)$$

Answer

$$(4,4)$$