If the midpoint between \((18, y)\) and \((20, -15)\) is \((19, -5)\), find the value of \(y\).
Answer (2)
( 18 , y ) an d ( 20 , − 15 ) i s ( 19 , − 5 ) ( x m , y m ) = [ 2 x 1 + x 2 , 2 y 1 + y 2 ] ( 19 , − 5 ) = [ 2 20 + 19 , 2 y − 15 ] ( 19 , − 5 ) = [ 19 , 2 y − 15 ] − 5 = 2 y − 15 / ∗ 2 − 10 = y − 15 ∣ + 15 y = − 10 + 15 y = 5 ( 19 , − 5 ) = [ 19 , 2 5 − 15 ] ( 19 , − 5 ) = ( 19 , − 5 ) A s w er : y = 5
The value of y is 5 as determined by using the midpoint formula for coordinates. By setting up equations based on the given midpoint and solving, we find that the midpoint condition holds true. Verification confirms that our solution is accurate.
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