i need help fast

Question

The endpoints of  are A(2, 3) and B(8, 1). The perpendicular bisector of  is , and point C lies on . The length of  is  units.

The coordinates of point C are (-6, 2)(5, 2)(6, -2)(10, 4). The slope of  is -3-1/31/33. The possible coordinates of point D are (4, 5)(5, 5)(6, 5)(8, 3) and (2, 1)(4, -1)(5, -1)(6, -1).

Answer 1

Here are some suggestions:

C is the midpoint of segment AB. (Use the midpoint formula).

The slope of AB can be found using the formula for the slope between two points.

The slope of CD is the negative reciprocal of the slope of AB (perpendicular lines).

The equation of the perpendicular bisector can be found using the point-slope formula. You know a point is passes through (C) and the slope.

Now where is D? It is √10 units from point C.

Determine the equation of the circle centered at C with a radius = √10.

Now find the points of intersection of the circle and the perpendicular bisector, using the substitution method. This will result in a quadratic equation, and two different values of x (assuming you substitute for y in the equation of the circle. Use those x -coordinates of point D to find the corresponding y coordinates.