Question

If the center of a circle is (3, 5) and end points of a diameter are (4, 7) and (2, y) then

the value of y is​

Answer 1

Answer:

$\boxed{\sf y = 3 }$

Step-by-step explanation:

Given that , the centre of a circle is ( 3 , 5 ) and the end points of the diameter are (4 , 7) and (2 ,y) . And we need to find the value of y .

• We know that the centre divides the diameter into two equal halves. So the centre will be the midpoint of the diameter . Henceforth we can use the Midpoint Formula .

$\sf\dashrightarrow Midpoint =\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\sf\dashrightarrow (3,5) = \bigg(\dfrac{4+2}{2},\dfrac{7+y}{2}\bigg) \\\\\sf\dashrightarrow (3,5) = \bigg(\dfrac{6}{2},\dfrac{7+y}{2}\bigg)\\\\\sf\dashrightarrow (3,5) = \bigg( 3, \dfrac{7+y}{2}\bigg)$

• Now on comparing the respective x and y coordinates, we have ,

$\sf\dashrightarrow 5 =\dfrac{7+y}{2}\\\\\sf\dashrightarrow 10 = 7 + y \\\\\sf\dashrightarrow y = 10 - 7 \\\\\sf\dashrightarrow \boxed{\pink{\sf y = 3 }}$

$\rule{200}2$