Choose the correct word that completes each statement about inscribing a square in a circle.
1 answer:
Answer:
1. Perpendicular
2. Isosceles
3. Never
Step-by-step explanation:
1. AC ⊥ BD because diameter of a square are perpendicular bisector of each other.
2. In Δ AOB , By using pythagoras : AB² = OA² + OB² .......( 1 )
In Δ COB , By using pythagoras : BC² = OC² + OB² ..........( 2 )
But, OA = OC because both are radius of same circle
So, by using equations ( 1 ) and ( 2 ), We get AB = BC ≠ AC
⇒ ABC is a triangle having two equal sides so ABC is an isosceles triangle.
3. The side can never be equal to radius of circle because the side of the square will be chord for the circle and in a circle chord can never be equal to its radius
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Step-by-step explanation:
The vertex form of the equation for a parabola is given by
where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as
Also, since the parabola passes through (4, -7), we can use this to find the value for a:
or
Therefore, the equation of the parabola is
The distance from point A(−9,−3) to the line y = x−6 is 8.5 units
<u>What is slope ?</u>
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
step 1
Find the slope of the perpendicular line to the given line
y=x-6 ---> given line
The slope is m=1
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
m1*m2 = -1
we have
m1=1
substitute
(1)*m2 = -1
so
m2 = -1
step 2
Find the equation of the perpendicular line to the given line
The equation in point slope form is
y-y1=m(x-x1)
we have
m=-1
(x1,y1)=(−9,−3)
substitute
y+3=-1(x+9)--> equation in point slope form
y+3= -x-9
y= -x-12---> equation in slope intercept form
step 3
Find the intersection point between the given line and the perpendicular line to the given line
we have the system of equations
y = x−6.
y= -x-12
Solve the system by graphing
The intersection point is (-3,-9)
see the attached figure
step 4
we know that
The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6
the formula to calculate the distance between two points is equal to
d=√[(y2-y1)² + (x2-x1)²]
substitute the values
d=√[(-9+3)² + (-3+9)²]
d= √72 units
simplify
d= 6√2 = 8.5 units
To learn more about the slope from the given link
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