#1
What is the distance between the points (3, 4) and (6, 8)?
6
ExplanationPythagorean theorem applied to find the length of the line segment.
#2
What is the midpoint of the line segment with endpoints (2, 5) and (8, 11)?
(8, 8)
ExplanationMidpoint formula: average of x-coordinates and average of y-coordinates.
#3
What is the distance between the points (-3, 0) and (4, 0)?
5
ExplanationAbsolute difference of x-coordinates, as they lie on the same horizontal line.
#4
If the slope of a line is undefined, what can be said about the line?
The line is vertical.
ExplanationUndefined slope indicates a vertical line.
#5
What is the slope of a line parallel to the y-axis?
undefined
ExplanationNo change in y-coordinate implies undefined slope.
#6
What is the slope of a horizontal line?
0
ExplanationHorizontal lines have no change in y-coordinate.
#7
If two points have the same x-coordinate, what can you say about their position?
They lie on the x-axis.
ExplanationCommon x-coordinate implies both points lie on the same horizontal line.
#8
What are the coordinates of the point which divides the line segment joining (-3, 4) and (5, -2) internally in the ratio 2:3?
(2, -2)
ExplanationInternal division formula applied to find the coordinates of the point.
#9
What is the equation of the line passing through the points (1, 2) and (5, 6)?
y = 2x - 1
ExplanationUsing point-slope form with one of the given points.
#10
What are the coordinates of the midpoint of the line segment joining (-4, 3) and (6, -5)?
(2, -1)
ExplanationMidpoint formula applied to find the coordinates of the midpoint.
#11
If the distance between two points is 10 units and one of the points is (3, 4), what could be the coordinates of the other point?
(6, 8)
ExplanationDistance formula applied with one known point to find the other.
#12
What is the slope of the line passing through the points (2, 3) and (6, 9)?
4
ExplanationUsing the slope formula between two given points.
#13
Find the equation of the perpendicular bisector of the line segment joining the points (2, 3) and (6, -1).
x + y = 7
ExplanationMidpoint and perpendicular slope used to find the equation.
#14
Find the distance between the parallel lines 2x - 3y + 4 = 0 and 2x - 3y - 7 = 0.
5
ExplanationPerpendicular distance between the lines is found using the formula.
#15
What is the slope of a line perpendicular to the line passing through the points (-2, 4) and (3, -5)?
-2
ExplanationNegative reciprocal of the slope of the given line.
#16
Find the equation of the line passing through the point (-3, 2) and perpendicular to the line 4x + 3y = 6.
3x - 4y = 18
ExplanationUsing slope and given point to determine the equation.
#17
What are the coordinates of the point which divides the line segment joining (-4, 5) and (6, -8) internally in the ratio 3:1?
(2, -2)
ExplanationInternal division formula applied to find the coordinates of the point.