The point with coordinates (p, q) will be rotated to the point with coordinates [(p - q)/sqrt(2), (p + q)/sqrt(2)].
True
zero Half the distance between them would be 4 units; so 3 units from P would not be close enough to Q to be equidistant.
q + p
If p then q is represented as p -> q Negation of "if p then q" is represented as ~(p -> q)
The possible coordinates of the midpoint depend on the coordinates of A and T and these depend on what these two points are and how they are related.If A = (p,q) and T = (r,s ) then the midpoint of AT has coordinates [(p+r)/2, ((q+s)/2].
Suppose the radius is r and the bearings of the two points, P and Q are p and q respectively. Then the coordinates of P are [r*cos(p), r*sin(p)] and the coordinates of Q are [r*cos(q), r*sin(q)]. The distance between these two points can be found, using Pythagoras: d2 = (xq - xp)2 + (yq - yp)2 where xp is the x-coordinate of P, etc.
The point with coordinates (p, q) will be rotated to the point with coordinates [(p - q)/sqrt(2), (p + q)/sqrt(2)].
If the coordinates of a point, before reflection, were (p, q) then after reflection, they will be (-p, q).
If you have the coordinates of two points, say P = (a,b) and Q = (c,d), then slope = (b-d)/(a-c) that is, the difference in the y coordinate of the two points divided by the difference in the x coordinate of the points taken in the same order.
If M P and Q are collinear and MP plus PQ equals MQ then P is between M and Q.
True
It would have been possible to give a simple answer if we could see what proportion of the way from A to B the question was about. But, thanks to the wonderful (not!) browser used by this site, we cannot and so this is a general answer.If the question was about p/q of the way, then the coordinates of the point are [(14*(q-p) + 4*p)/q, (1*(q-p) + 23*p)/q].
Points for "Q" in Scrabble
Suppose you have the points with coordinates (p, q) and (r, s) then, provided p is different from r, the slope of the line is (q - s)/(p - r) = m, say. Then, if (x, y) is any point on the line, (x - s)/(y - r) = m That, after simplification, is the linear equation of the line. This will be a lot simpler when you have numerical values for p, q, r and s rather than work algebraically throughout. If p is not different from r, then the equation is x = p (or r), a vertical line.
coplanar
The coordinates of the mid points are the means of the pairs of coordinates of the two end points. Thus, if P = (px, py, pz) and Q = (qx, qy, qz) then the midpoint of PQ is [(px+qx)/2, (py+qy)/2, (pz+qz)/2]. The result can be simplified for 2-dimensional space, or extended to more dimensions.