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The equation of the perpendicular bisector of BC with B(-2, 1), and C(4, 2) is y = 7.6 - 6•x
<h3>Which method can be used to find the equation of the perpendicular bisector?</h3>The slope, <em>m</em>, of the line BC is calculated as follows;
- m = (2 - 1)/(4 - (-2)) = 1/6
The slope of the perpendicular line to BC is -1/(1/6) = -6
The midpoint of the line BC is found as follows;
The perpendicular bisector is the perpendicular line constructed from the midpoint of BC.
The equation of the perpendicular bisector in point and slope form is therefore;
(y - 1.5) = -6•(x - 1)
y - 1.6 = -6•x + 6
y = -6•x + 6 + 1.6 = 7.6 - 6•x
Which gives;
- y = 7.6 - 6•x
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The vertex form of the function is y = (x + 8)² - 71
The vertex is (-8 , -71)
Step-by-step explanation:
The vertex form of the quadratic equation y = ax² + bx + c is
y = a(x - h)² + k, where
- (h , k) are the coordinates of the vertex point
- a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept
- k is the value of y when x = h
∵ y = x² + 16x - 7
∵ y = ax² + bx + c
∴ a = 1 , b = 16 , c = -7
∵
∴
∴ h = -8
To find k substitute y by k and x by -8 in the equation above
∵ k is the value of y when x = h
∵ h = -8
∴ k = (-8)² + 16(-8) - 7 = -71
∵ The vertex form of the quadratic equation is y = a(x - h)² + k
∵ a = 1 , h = -8 , k = -71
∴ y = (1)(x - (-8))² + (-71)
∴ y = (x + 8)² - 71
∵ (h , k) are the coordinates of the vertex point
∵ h = -8 and k = -71
∴ The vertex is (-8 , -71)
The vertex form of the function is y = (x + 8)² - 71
The vertex is (-8 , -71)
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