Please help me with this.

Mathematics

1 answer:

inna [77]3 years ago

3 0

Answer:

Plot and connect (5,4), (3,0) and (7,0).

Step-by-step explanation:

This is in factored form and can be graphed directly from the equation. The equation shows the x-intercepts.

The x-intercepts are found by solving for x using the zero product rule.

(x-3)=0 so x = 3

(x-7) = 0 so x = 7

The intercepts are (3,0) and (7,0). Plot the points. The vertex will occur halfway between these points. 7-3 / 2 = 4/2 = 2. This means the axis of symmetry is at x = 5 and this is the x-coordinate of the vertex too.

Substitute x = 5 into the equation and solve for y.

-(5-3)(5-7) = -(2)(-2) = 4

The vertex is (5,4). Plot it and connect the points.

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The endpoints of AB are A(2, 3) and B(8, 1). The perpendicular bisector of AB is CD, and point C lies on AB. The length of CD is

marysya [2.9K]

Comment
If C lies on AB Then it must be the midpoint of AB because CD is the Perpendicular Bisector of AB

Midpoint
A(2,3) B(8,1)
Midpoint formula = (x1 + x2)/2 + (y1 + y2)/2
Midpoint = (2 + 8)/2 + (3 + 1) / 2
Midpoint = 10/2 + 4/2
Midpoint = (5,2) <<<<< answer

Slope AB
slope = (y2 - y1)/(x2 - x1)
slope = (3 - 1) / (2 - 8)
slope = 2/-6 = -1/3

Slope CD
CD_slope * AB_slope = - 1
CD_slope * -1/3 = -1 multiply both sides by - 3
CD_slope * 1 = - 1 * -3
CD_slope = 3 <<<<< Slope CD Answer

Equation CD
Given the midpoint of AB which is C( and the slope of CD
y = 3x + b
2 = 3*5 + b
b = - 13
Equation y = 3x - 13

Using Distance to get D
d^2 = (x1 - x2)^2 + (y2 - y1)'^2
d^2 = (x2 - 5)^2 + (y2 - 2)^2
y2 = 3*x2 - 13
10 = x2^2 - 10x2 + 25 + (3x2 - 13 - 2)^2
10 = x2^2 - 10x2 + 25 + (3x2 - 15)^2
10 = x1^2 - 10x2 + 25 + 9x^2 - 90x2 + 225
10 = 10x2^2 - 100x2 +250
0 = 10x2^2 - 100x2 + 240 Divide through by 10
0 = x2^2 - 10x^2 + 24
0 = (x2 - 6)(x2 - 4)

x2 = 6 or
x2 = 4

Using y2 = 3x - 13
for x2 = 4
then y2 = 3(4) - 13
y2 = - 1

for x2 = 6
y2 = 3*6 - 13
y2 = 5

Possible Answers for D
D = (4,-1)
D = (6,5)

I've included a graph to show a graphical solution.

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