Acircle has a diameter with endpoints at 15 + 25i and –25 – 17i. which point is also on the circle? –15 +21i 0 + 0i 15 + 17i 16 + 24i

Answers

D

Step-by-step explanation:

Edge

The point 16+24i is the point satisfying the equation

Hence, Option D is correct.

Step-by-step explanation:

We will find mid-point from end points given.

Mid-point formula: (x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

On substituting the values we will get:

(x,y)=(\frac{-25+15}{2},\frac{-17+25}{2})

(x,y)=(-5,4)

Now, we have general equation of circle:

(x-a)^2+(y-b)^2=r^2

We will find r that is distance from mid-point to end oint using distance formula

\text{distance formula}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Here, x_1=-5,x_2=-25,y_1=4,y_2=-17

On substituting the values we get:

\text{distance formula}=\sqrt{(-25+5)^2+(-17-4)^2}

\text{distance formula}=\sqrt({20}^2+{21}^2)

\text{distance}=\sqrt{841}

Hence, r^2=841

Substituting the values in general equation we get:

(x-(-5))^2+(y-4)^2=841

[tex]\Rightarrow(x+5)^2+(y-4)^2=841[tex]

And when we substitute x=16 and y=24 the equation will be satisfied

and a=-5 and b=4

Hence, will lie on the circle

Therefore, option D is correct.

The answer is: D, 16+24i!

Option 4 : 16+24i

Step-by-step explanation:

Given a circle has a diameter with end points at(15+25i) and (-25-17i)

Centre would be the mid point of these two points

Centre = (\frac{15-25}{2} ,\frac{25-17}{2} )\\= -5+4i

Out of given four points to find which point lies on the circle

If a point lies on the circle then it would have distance from centre equal to radius.

Radius = distance between two given points/2

=\frac{1}{2} \sqrt{(15+25)^2+(25+17)^2} \\=\frac{58}{2} \\=29

Let us calculate distance form each point.

i)-15+2i:  distance from -5+4i= 10.19

ii) 0+0i : distance from -5+4i = 6.40

iii) 15+17i :  Distance from -5+4i = 23.85

iv) 16+24i: distance from -5+4i= 29

Hence only 4th point lies on the circle



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