Question

If (0,0)is the centre of a circle and (2,3) is one endpoint of its diameter then find the other end point.
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Answer 1

Answer:

Step by step solution :STEP1:Equation at the end of step 1 (22m2 - 24m) + 36 = 0 STEP2:STEP3:Pulling out like terms

3.1 Pull out like factors :

4m2 - 24m + 36 = 4 • (m2 - 6m + 9)

Trying to factor by splitting the middle term

3.2 Factoring m2 - 6m + 9

The first term is, m2 its coefficient is 1 .

The middle term is, -6m its coefficient is -6 .

The last term, "the constant", is +9

Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9

Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is -6 .

-9 + -1 = -10 -3 + -3 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and -3

m2 - 3m - 3m - 9

Step-4 : Add up the first 2 terms, pulling out like factors :

m • (m-3)

Add up the last 2 terms, pulling out common factors :

3 • (m-3)

Step-5 : Add up the four terms of step 4 :

(m-3) • (m-3)

Which is the desired fact

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Answer 2

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One end of diameter of the circle = (3,2)

Center of the circle = (0,0)

Let, the other end of diameter of the circle = (x,y)

Since , center is the mid-point of the diameter of the circle

• (0,0)=( 3+x / 2 , 2+y / 2)
• 23+x =0 and 22+y =0
• 3+x=0 and 2+y=0
• x=−3 and y=−2

Hence, the other end of diameter of the circle =(−3,−2)