Question

two vertices of a triangle are 3,5 and -4, -5. if the centroid of the triangle is 4,3 find the third vertex​

Answer 1

ANSWER

THIRD VERTEX=(13, 9)

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STEP BY STEP EXPLANATION

LET THIRD VERTEX BE (x,y)

TWO VERTICES OF TRIANGLE= (3,5);(-4,-5)

CENTROID OF TRIANGLE=(4,3)

$( \frac{x1 + x2 + x3}{3} \: \: \: \frac{y1 + y2 + y3}{3} ) = (4 \: \: 3) \\ \\ ( \frac{3 - 4 + x}{3} \: \: \: \frac{5 - 5 + y }{3} = (4 \: \: 3) \\ \\ ( \frac{x - 1}{3} \: \: \: \frac{y}{3} ) = (4 \: \: 3)$

ON COMPARING

$\frac{x - 1}{3} = 4 \\ \\ x - 1 = 12 \\ \\ x = 12 + 1 \\ \\ x = 13$

$\frac{y}{3} = 3 \\ \\ y = 9$

THIRD VERTEX=(13,9)

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Answer 2

Answer:

Third vertex = (13,9)

Step-by-step explanation:

Let third vertex be (x,y)

Two vertices of triangle = (3,5),(-4,-5)

centroid of triangle = (4,3)

( x1 + x2 + x3 /3 y1 + y2 + y3 / 3) (4,3)

( 3 - 4 + x / 3 5 - 5 + y = (4,3)

( x - 1 / 3 y / 3 ) = (4,3)

on comparing

x - 1 / 3 = 4

x - 1 = 12

x = 12 + 1

x = 13

y / 3 = 3

y = 9

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silentlover45.❤️