BTGmoderatorLU wrote:The line represented by the equation y = 4 - 2x is the perpendicular bisector of the line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?
A. (-4, 1)
B. (-2, 2)
C. (0, 1)
D. (0, -1)
E. (2, 0)
The OA is D.
Please, can anyone assist me with this PS question? I don't know how can I solve it. I need help. Thanks!
The equation provided by the question stem, y = 4 - 2x, is written in slope-intercept form, y = mx + b.
In the slope-intercept equation of a line, the coefficient of the x-term represents the line's slope, and 'b' represents the line's y-intercept.
Thus, the slope of the line is -2, and the line intersects the y-axis at point (0, 4).
Use this information to quickly sketch the line in an xy-coordinate plane, so that it passes through points (0, 4), (1, 2), (2, 0), and so on.
Line segment RP is perpendicular to the line with equation 'y = 4 - 2x'.
The slopes of perpendicular lines are negative reciprocals, so the slope of line segment RP must be 1/2.
Plot point R at coordinates (4, 1), and then use the slope of line segment RP to quickly sketch a line passing through points (4, 1), (2, 0), and (0, -1).
The line and line segment intersect at point (2, 0).
Since the line bisects line segment RP, the distance from the line to point R must be equal to the distance from the line to point P.
Point R is 2 units to the right and one unit above point (2, 0), so point P must be 2 units to the left and one unit below point (2, 0).
The correct answer is choice
D.
