Find the coordinates of 3rd vertex of triangle ABC if A(-5,-7),B(4,-3) and the coordinates of the centroid lies at (-1,2) ? (Please explain it step by step)

Question

Find the coordinates of 3rd vertex of triangle ABC if A(-5,-7),B(4,-3) and the coordinates of the centroid lies at (-1,2) ?  (Please explain it step by step)

Answer

A(-5,-7),B(4,-3)C(x3,y3) let G(-1,2)centroid :_is a point where three median of a triangle are intersect each other let coardinates of centroid G(-1,2)X=X1+X2+X3 by 3 -1=-5+4+x by 3-3=-1+x-3+1=xx=2y= y1+y2+y3 by 32=(-7)+(-3)+(y) by 32=-7-3+y by 3 2×3=-10+y 6=-10+y6+10=y y=16 C(-2,16)

Answer

Guys it's so simple. Let A(3.−5), B(−7,4)and C(x,y). Its given tht : Centroid 'O' (2, -1)Centroid'O'=x1+x2+x3÷3, y1+y2+y3÷3⟹(3−7+x)÷3=2{u can solve this} x=10⟹(−5+4+y)÷3=−1 ~~y=-2. So, (10,-2)

Answer

Explain step by step pls

Answer

(10,-2)

Answer

Process

Answer

(10,-2)

Answer

Thanks Manoj

Answer

Step 1: Understanding the Centroid Formula
The centroid (G) of a triangle with vertices A(x1, y1), B(x2, y2), and C(x3, y3) can be calculated using the formula:
G = ((x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3).
Step 2: Given Points
- A = (-5, -7)
- B = (4, -3)
- G = (-1, 2)
Step 3: Setting Up the Equations
Let C = (x, y). From the formula for the centroid, we can set up the following equations:
- For x-coordinate:
(-5 + 4 + x) / 3 = -1
- For y-coordinate:
(-7 - 3 + y) / 3 = 2
Step 4: Solving for x
Multiply the x-coordinate equation by 3:
-5 + 4 + x = -3
-1 + x = -3
x = -3 + 1
x = -2
Step 5: Solving for y
Multiply the y-coordinate equation by 3:
-7 - 3 + y = 6
-10 + y = 6
y = 6 + 10
y = 16
Step 6: Conclusion
The coordinates of the 3rd vertex C are:
C = (-2, 16)
Thus, the final answer is:
C = (-2, 16).

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