Question

(a)Two vertices of a triangle are (-1,4), and (5,2). If the centroid is (0,3) find the third vertex ?​

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Answer 1

Answer:

-4;3

Step-by-step explanation:

-1+5+x/3=0

4+x=0

x=-4

4+2+y/3=3

6+y= 9

y= 9-6=3

Answer 2

Answer:

• The third vertex is (-4, -15).

Step-by-step explanation:

Let the third vertex be (x,y) then the coordinates of the centroid of circle are :

$\bigg \lgroup \tt \frac{ - 1 + 5 + x}{3} , \frac{4 + 2 + y}{3} \bigg \rgroup \\ \\ \implies \: \bigg \lgroup \tt \: \frac{4 + x}{3} , \frac{6 + y}{3}\bigg \rgroup \\ \\ \tt \: now, \\ \implies \bigg \lgroup \tt \: \frac{4 + x}{3} , \frac{6 + y}{3}\bigg \rgroup = (0, - 3) \\ \\ \implies \tt \frac{4 + x}{3} = 0 \: \: and \: \frac{6 + y}{3} = - 3 \\ \\ \implies \tt \: 4 + x = 0 \: \: and \: \: y + 6 = - 9 \\ \\ \implies \tt \: x = - 4 \: \: and \: \: y - 15 \\ \\ \tt \pink{hence, \: the \: third \: vertex \: is \: ( - 4, - 15)}$