I really need help with this.
1 answer:
9514 1404 393
Answer:
a. (1.4, 2.6)
b. (3, 2)
Step-by-step explanation:
a. The circumcenter is the intersection point of the perpendicular bisectors of the sides of the triangle.
For points X(a, b) and Y(c, d), the perpendicular bisector of XY can be written as ...
(c -a)(x -(c+a)/2) +(d -b)(y -(d+b)/2) = 0
Then the equation of the perpendicular bisector of MN is ...
(-2-4)(x -(-2+4)/2) +(4-0)(y -(4+0)/2) = 0
-6(x -1) +4(y -2) = 0
3x -2y = -1 . . . . divide by -2 and put in standard form
Similarly, the perpendicular bisector of NO is ...
(0-(-2))(x -(0-2)/2) +(6 -4)(y -(6+4)/2) = 0
2(x +1) +2(y -5) = 0
x + y = 4 . . . . divide by 2 and put in standard form
So, the point of intersection is ...
(3x -2y) +2(x +y) = (-1) +2(4) . . . . . add twice the 2nd equation to the 1st
5x = 7 . . . . . . simplify
x = 1.4 . . . . . . divide by 5
y = 4-1.4 = 2.6 . . . . . find y from the second equation
The coordinates of the circumcenter are (1.4, 2.6).
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b. The centroid is the average of the vertex coordinates.
centroid = (A +B +C)/3 = ((1, 2) +(3, 4) +(5, 0))/3 = (1+3+5, 2+4+0)/3 = (9, 6)/3
centroid = (3, 2)
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The negative solution is x = –1.
Solution:
Let the number be x.
Square of a number = x²
3 times a number = 3x
Difference of square of a number and 4 = 3 times that number
Subtract 3x from both sides of the equation, we get
–3x can be written as x – 4x.
1st bracket have common term x and bracket have –4 common term.
Take common term x + 1 outside.
<em>By zero factor principle, if AB = 0 then A = 0 or B = 0.</em>
x + 1 = 0, x – 4 = 0
x = –1, x = 4
The negative solution is x = –1.