Answer:
The correct option is;
D(4, 4)
Step-by-step explanation:
The given coordinates of the points are, A(2, 3) B(8, 7), C(6, 1), therefore, the coordinates of the point D that will make CD perpendicular to AB will have a slope = -1/m, where, m = the slope of the line segment AB
The formula for finding the slope, m, of a segment, given the coordinates of two points on the straight line segment (x₁, y₁), (x₂, y₂)
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Therefore, for, the segment AB, we have;
m = (7 - 3)/(8 - 2) = 4/6 = 2/3
m = 2/3
Therefore, to make the segment AB perpendicular to the segment CD, the slope of the segment CD will be -1/m = -1/(2/3) = -3/2
The equation of the segment CD in point and slope form is therefore;
y - 1 = -3/2×(x - 6)
y - 1 = -3·x/2 + 9
The standard form of the equation of the segment CD is therefore;
y = -3·x/2 + 9 + 1 = -3·x/2 + 10
y = -3·x/2 + 10
The point that satisfies the above equation is the point (4, 4) because;
4 = -3 × 4/2 + 10
The correct option is therefore, D(4, 4).
