Question

A circle 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

Answer 1

Answer:

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