Question

The equation of the right bisector of the line segment joining the points (7,4) and (-1, -2) ​

Answer 1

Answer: y = -(4/3)x + 5.

Step-by-step explanation: First, find the equation of the line connecting (7, 4) and (-1, -2). Using the slope formula, (y2 - y1)/(x2 - x1) --> (-2 - 4)/(-1 - 7) --> (-6)/(-8) --> 3/4. Then, we have to find the slope perpendicular (or right) to 3/4 which is its negative reciprocal, or -4/3. Next, we must find the midpoint of the line segment two in order to bisect it. The midpoint formula is [(x2 + x1)/2], [(y2 + y1)/2], so therefore, [(-1 + 7)/2], [(-2 + 4)/2] --> [6/2], [2/2] --> (3, 1). Now we can use the point-slope formula to form an equation using a slope and a point. y - y1 = m(x - x1) --> y - 1 = (-4/3)(x - 3) --> y - 1 = (-4/3)x + 4 --> y = -(4/3)x + 5.