A line segment has end points A (-12, -11) and B (6, 19). Find the three points that divide AB into four equal pieces. A) show that the line segment with end points A (5,3) and B (5 ,-5) is a chord of the circle X to the power of 2 + Y to the power of two = 34
To determine the three points that divide AB into 4 equal parts, we shall find a point X on AB such that X is the midpoint of AB. Then we shall find a point Y on AX such that Y is the midpoint of AX. Finally, we shall find a point Z such that Z is the midpoint of XB
Midpoint of AB
Midpoint of AB
Midpoint of AX
Midpoint of AX
Midpoint of BX
Midpoint of BX
Equation of circle :
To show that line AB is a chord of the circle, we shall show that one of the points lie on the circle, and the midpoint of line AB is not the centre of the circle
Let
Hence, lies on the circle
Midpoint of AB
Midpoint of AB
From , it is evident that the centre of the circle is
Hence, line AB is a chord of the circle,
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