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Quandaries & Queries
Q & Q
 Topic: midpoint
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The midpoints of the sides of a quadrilateral 2016-02-05
From Andrea:
The segments, joining, in order the midpoints of consecutive sides of a quadrilateral form a parallelogram.
Two circles 2012-02-08
From crisfe:
find the point where the common cord of the circles x2+y2=25, x2+y2-12x-6y+35=0 process there line centers. what point they intercepts?
The midpoints of two sides of a triangle 2009-03-17
From Manis:
Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it.
The midpoint o a line segment 2008-11-15
From Jane:
The vertices of a triangle are at (1,7), (6,-1) and (0,3). Find the coordinates of the midpoints of the sides.
The midpoints of the sides of a quadrilateral 2008-07-22
From JOEL:
A QUADRILATERAL A,B,C,D HAS THE CO -ORDINATE [2,5],[8,7],[10,3]&[0,1] RESPECTIVLY [B,E,G,H] ARE THE MID POINTS OF THE SIDES AB,BC,CD&DA RESPECTIVLY FIND THE MID POINTS OF [FG]&[FH]
Slopes of a triangle's medians 2007-08-11
From Gina:
I am trying to help my daughter with this, but I am very weak in Math.Please help! Find slopes of the medians of a triangle whose vertices are P(1,3), Q(3,5), and R(6,2)
The centroid of a triangle 2006-01-18
From Andrea:
I am trying to find the centriod of a triangle. I have been given the three vertices of the triangle: A (-25, -20), B (-5, -40), and C (15, 30). I believe I calculated the correct midpoints: AB(E) (-5, 5), BC(D) (5, -5), and AC(F) (-15, -30). When I graphed these points I came up with the solution (-5, -10), but I can't seem to write the answer out (equations of the lines, etc) correctly. Any help would be greatly appreciated!
Equidistant from the points (2,-1,1) and (0,1,3) 2005-11-06
From Roy:

Find the point on the y-axis that is equidistant from the points (2,-1,1) and (0,1,3).

Find the point not on the y-axis that is equidistant from the points (2,-1,1) and (0,1,3).

Answered by Penny Nom and Walter Whiteley.
The mean house price 2003-09-10
From Carol:

Question:
I have to find the mean from the following example:

Price Range £000 No of Houses
55 and under 60 3
60 and under 65 6
65 and under 70 13
70 and under 80 21
80 and under 100 15
100 and under 130 7
130 upwards 1

I know when calculating the mean you use the mid points of the classes, but how does this work for the 130 upwards class? Also, does this still work given the difference in the classes (ie. 1st class is 5, 5th class is 20, etc). Any help to get me started would be greatly appreciated.

Prove that the medians of triangle PQR meet in a central point G. 2001-11-11
From Jessica:
Use a scalene triancle with one point (0,b) on the y axis, another point (2c, 0) on the x-axis and the last point, (2a,0) on the x-axis. Prove that the medians of triangle PQR meet in a central point G.