Mathematics 2014 JAMB Past Questions - Question 35: Calculate the mid point of the line segment y-4x+3=0 which lies between the x-axis and y axis.

Correct Answer

B

Explanation

y = 4x +3=0 (given)when y = 0, 0-4x +3=0-4x = -3 x = 3/4To find the midpoint of the line segment that lies between the x-axis and y-axis, we need to find the coordinates of the two endpoints of the line segment.First, let's find the x-intercept by setting y = 0 in the equation y - 4x + 3 = 0:0 - 4x + 3 = 0Simplifying the equation, we get:-4x + 3 = 0-4x = -3Dividing both sides of the equation by -4, we find:x = 3/4So, the x-coordinate of the x-intercept is 3/4.Next, let's find the y-intercept by setting x = 0 in the equation y - 4x + 3 = 0:y - 4(0) + 3 = 0Simplifying the equation, we get:y + 3 = 0y = -3So, the y-coordinate of the y-intercept is -3.Now, we can find the midpoint of the line segment by taking the average of the x-coordinates and the average of the y-coordinates.Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)Midpoint = ((3/4 + 0) / 2, (-3 + 0) / 2)Simplifying further, we have:Midpoint = (3/8, -3/2)Therefore, the midpoint of the line segment that lies between the x-axis and y-axis is (3/8, -3/2).so the line cuts the x-axis at the point (3/4, 0)when x = 0, y - 4(0) +3 = 0y + 3 = 0 y = -3so the line cuts the y-axis at the point (0,3)Hence the midpoint of the line y - 4x +3=0 whichlies between the x-axis and the y-axis is<1//2 (xsup1 + xsup2), 1/2 (ysup1 +ysup2)<1/2 (3/4 +0), 1/2 (0 + -3)> = <1/2 (-3)>= <3/8, -3/2