SOLUTION: the equation of a line 3x-2y=20 what point on the line is equidistant from the points A(1,-1) and B(1,8)

Question 1106795: the equation of a line 3x-2y=20 what point on the line is equidistant from the points A(1,-1) and B(1,8)
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
Here is a start.
The line is which is a general point ( , ).

Using Distance Formula and squaring both sides, Line to A equals Line to B;

Simplify and solve for x;
.
.

.
.
Answer by ikleyn(52890) (Show Source): You can put this solution on YOUR website!
.
the equation of a line 3x-2y=20 what point on the line is equidistant from the points A(1,-1) and B(1,8)
~~~~~~~~~~~~~~~~~

The point under the question is the intersection point of the given line with the perpendicular bisector to the line segment connecting the given points A(1,-1) and B(1,8). Notice that the line connecting these points is VERTICAL line x = 1. Hence, the perpendicular bisector is the horizontal line y = 3.5 (where 3.5 = ). The intersection point is that you will obtain after substituting y = 3.5 into the equation of the given line: 3x - 2y = 20 at y = 3.5 becomes 3x - 2*3.5 = 20 ====> 3x = 20+7 = 27 ====> x = = 3. Hence, the point you are seeking for is (2,3.5). Thus you can solve this problem MENTALLY, without solving ANY equations.

RELATED QUESTIONS
the equation of line 3x-2y =20 what point on the line is equidistant from the points A(1, (answered by ikleyn)
1. Write and equation for a graph that is the set of all points in the plane... (answered by stanbon)
Write an equation for a graph that is the set of all points in the plane equidistant from (answered by poliphob3.14)
#1. Find a point on the line 2x + y = 8 that is equidistant from the coordinate axes.... (answered by jim_thompson5910)
Write an equation for a graph that is the set of all points in the plane that are... (answered by josgarithmetic)
Find a point on the line {{{ x+2y=8 }}} that is equidistant from point (3,8) and... (answered by josgarithmetic,Edwin McCravy,ikleyn)
write the equation whose graph is the set of all points in the plane equidistant from the (answered by KMST)
Find the coordinates of the point on the line y = x - 9 which is equidistant from the... (answered by Alan3354)
Two points have coordinates A(1,-3) and B(-3,5).Find the equation of the perpendicular... (answered by ewatrrr)