The line 2x+3y+k=0 passes through the mid point of the line segment with end points (5,7) and (3,5) What - Maths - Coordinate Geometry

Question

The line 2x+3y+k=0 passes through the mid point of the line segment
with end points (5,7) and (3,5) What is the value of k?

Manbar Singh · Accepted Answer

We know that coordinates of the midpoint x, y of a line segment joining points x1,y1 and x2, y2 isx = x1 + x22   and  y = y1 + y22Now, coordinates of the mid point of the line segment joining 5,7 and 3, 5 is P5+32, 7+52 = P4,6
Since 2x + 3y + k = 0 passes through P4,6, then it must satisfy the given equation
Now, 2×4 + 3×6 + k = 0⇒8 + 18 + k = 0⇒k = -26

The line 2x+3y+k=0 passes through the mid point of the line segment with end points (5,7) and (3,5). What is the value of k?