Length and midpoint：练习题

In a coordinate plane, point \(P\) has coordinates \((-4, 2)\) and point \(Q\) has coordinates \((2, 10)\).
Calculate the distance between point \(P\) and point \(Q\).

The midpoint of the line segment joining \(A(x, 5)\) and \(B(6, y)\) is \(M(4, 2)\).
Find the values of \(x\) and \(y\).

A square \(ABCD\) has vertices \(A(1, 1)\) and \(C(5, 5)\) as opposite corners.
Find the coordinates of the center of the square and the length of one side of the square.

A line segment connects the points \(A(2, 7)\) and \(B(8, -1)\).
Find the coordinates of the midpoint of the line segment \(AB\).

The gradient of a line segment joining point \(A(1, 2)\) and point \(B(5, p)\) is \(\frac{3}{4}\).
Calculate the length of the line segment \(AB\).

Point A has coordinates \((7, -2)\) and point B has coordinates \((-3, 6)\). Calculate the coordinates of the midpoint of the line segment AB.

A triangle has vertices at \(A(1, 2)\), \(B(1, 6)\), and \(C(4, 2)\). Calculate the perimeter of triangle ABC.

The point \(M(5, 4)\) is the midpoint of the line segment \(AB\). Point \(A\) has coordinates \((2, k)\) and the length of the line segment \(AB\) is \(10\) units. Find the two possible values of \(k\).

The coordinates of two points are A \((-2, 5)\) and B \((4, 11)\).
(a) Find the coordinates of the midpoint, M, of the line segment AB.
(b) Calculate the exact length of the line segment AB.
(c) Point C lies on the same line such that B is the midpoint of AC. Find the coordinates of C.

The points A and B have coordinates \((3, 2)\) and \((6, 6)\) respectively.
(a) Calculate the length of the line segment AB.
(b) Find the coordinates of the midpoint of AB.
(c) Point C lies on the y-axis such that the distance AC is equal to the distance AB. Find the possible coordinates for point C.