What are the coordinates of the centroid of a triangle with vertices D(0,1),E(2,6), and F(7,2) enter your answer in the boxes
1 answer:
The coordinates of centroid of given triangle are: (3,3)
Step-by-step explanation:
Given
D(0,1) = (x1,y1)
E(2,6) = (x2,y2)
F(7,2) = (x3,y3)
The centroid of a triangle when the vertices are known is given by:
Putting the values
Hence,
The coordinates of centroid of given triangle are: (3,3)
Keywords: Triangle, centroid
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Answer: unit and 18 unit
Step-by-step explanation:
Let ABCD is a trapezoid where AB and CD are the bases. ( In which AB is greatest base which shown in below figure)
AD and BC are the legs of the trapezoid ABCD.
Now, we have ( According to the question ),
AB = 18 unit, BC = 7 unit, AD = 3 unit and DC = 11 unit.
Here the leg AD extends from point D.
Similarly leg BC extends from point C.
Let they meet at point P ( shown in below diagram)
Since In triangles PAB and PDC,
∠PDC ≅ ∠PAB ( because DC ║ AB )
And, ∠ PAB ≅ ∠ PBA
∠DPC ≅ ∠ APB ( reflexive)
Therefore, By AAA similarity postulate,
Thus, By the definition of similarity,
( because PA = PD+DA)
⇒ 18 PD = 11 PD +33
⇒7PD = 33
⇒ PD = 33/7
Again by the definition of similarity,
( because PB = PC + CB)
⇒ 18 PC = 11 PD +77
⇒7PC = 77
⇒ PC = 11
Thus, PA = PD+DA = 33/7 + 3 =
And, PB = PC + CB = 11 + 7 = 18
