Calculate the mid point of the line segment y – 4x + 3 = 0, which lies between the x-axis and y-axis.
-
A.
(begin{pmatrix} 3 & -3 \ 8 & 2 end{pmatrix}) -
B.
(begin{pmatrix} 3 & 3 \ 8 & 2 end{pmatrix}) -
C.
(begin{pmatrix} -2 & 2 \ 2 & 2 end{pmatrix}) -
D.
(begin{pmatrix} -2 & 3 \ 3 & 2 end{pmatrix})
Correct Answer: Option A
Explanation
y – 4x + 3 = 0
When y = 0, 0 – 4x + 3 = 0
Then -4x = -3
x = 3/4
So the line cuts the x-axis at point (3/4, 0).
When x = 0, y – 4(0) + 3 = 0
Then y + 3 = 0
y = -3
So the line cuts the y-axis at the point (0, -3)
Hence the midpoint of the line y – 4x + 3 = 0, which lies between the x-axis and the y-axis is;
([frac{1}{2}(x_1 + x_2), frac{1}{2}(y_1 + y_2)])
([frac{1}{2}(frac{3}{4} + 0), frac{1}{2}(0 + -3)])
([frac{1}{2}(frac{3}{4}), frac{1}{2}(-3)])
([frac{3}{8}, frac{-3}{2}])
There is an explanation video available below.