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the complete question is
<span>Point A has an x coordinate of −2 and lies in a circle with a center at (0, 0) and a radius of 5.
To the nearest tenth, what is the y-coordinate for point A?
A: 4.5
B: 4.6
C: 4.7
D: 4.8
see the attached figure
we know that
the equation of the circle is
(x-h)</span>²+(y-k)²=r²
(h,k) is the center---------> (h,k) is the point (0,0)
r=5 units
so
(x-h)²+(y-k)²=r²--------> (x-0)²+(y-0)²=5²------> x²+y²=25
substitute the value of x=-2 in the equation
(-2)²+y²=25------> y²=25-4------> y=(+/-)√21
the y coordinate of point A is positive----> see the picture
therefore
y=√21-----> 4.58-----> y=4.6
the answer is
the y-coordinate for point A is 4.6
<span>Point A has an x coordinate of −2 and lies in a circle with a center at (0, 0) and a radius of 5.
To the nearest tenth, what is the y-coordinate for point A?
A: 4.5
B: 4.6
C: 4.7
D: 4.8
see the attached figure
we know that
the equation of the circle is
(x-h)</span>²+(y-k)²=r²
(h,k) is the center---------> (h,k) is the point (0,0)
r=5 units
so
(x-h)²+(y-k)²=r²--------> (x-0)²+(y-0)²=5²------> x²+y²=25
substitute the value of x=-2 in the equation
(-2)²+y²=25------> y²=25-4------> y=(+/-)√21
the y coordinate of point A is positive----> see the picture
therefore
y=√21-----> 4.58-----> y=4.6
the answer is
the y-coordinate for point A is 4.6
In geometry, it would be always helpful to draw a diagram to illustrate the given problem.
This will also help to identify solutions, or discover missing information.
A figure is drawn for right triangle ABC, right-angled at B.
The altitude is drawn from the right-angled vertex B to the hypotenuse AC, dividing AC into two segments of length x and 4x.
We will be using the first two of the three metric relations of right triangles.
(1) BC^2=CD*CA (similarly, AB^2=AD*AC)
(2) BD^2=CD*DA
(3) CB*BA = BD*AC
Part (A)
From relation (2), we know that
BD^2=CD*DA
substitute values
8^2=x*(4x) => 4x^2=64, x^2=16, x=4
so CD=4, DA=4*4=16 (and AC=16+4=20)
Part (B)
Using relation (1)
AB^2=AD*AC
again, substitute values
AB^2=16*20=320=8^2*5
=>
AB
=sqrt(8^2*5)
=8sqrt(5)
=17.89 (approximately)
