This document contains a series of problems involving finding coordinates of midpoints of line segments, calculating gradients and lengths of lines, and determining missing coordinate values given other information about the lines. There are multiple sets of labeled points and questions about finding various geometric properties of the lines connecting those points.

1. B(5, 6)
F(9, 2 )
C(0, 4)
E(-3, -4)
A(-7, -2) D(4, 0)
)
Find the y-coordinate of
Find the x-coordinate of
the midpoint of the line
Find the x-coordinate of the midpoint of the line
segment AB
the midpoint of the line segment EF
segment CD
K(-3, 8)
B(6, 5)
I(-1, 2) J(5, 2)
)
L(-3, -2)
A(-2, -2)
Calculate the y- Calculate the x- Calculate the y-
coordinate of the coordinate of the coordinate of the
midpoint of the line midpoint of the line midpoint of the length
segment GH segment IJ segment KL
B(3, y)
D(1, y) E(-4, 5)
)
C(-3, 0)
A(-1, -2) F(x, -5)
The gradient of the line The gradient of the line The gradient of the line
AB is 2, what is the value CD is 3, what is the value is -2, what is the value of
of the y coordinate at B? of the y coordinate at D? the x coordinate at F?
BAP – 1008HF Gradient & Length Game

2. A (6, 10)
E(-2, 4)
C (-3, 8)
B (-2, -5)
F(4, -4)
D (3, -4)
Find the length of the Find the length of the Find the length of the
line AB line CD line EF
G (5, 7) K (-3, 3)
I (3, 10)
L (0, -2)
H (-7, -2)
J (-2, -2)
Find the length of the Find the length of the Find the length of the
line GH line IJ line KL
C (-2, 8)
B (4, 9) F (2, 6)
A (-3, 2)
D (2, 0)
E (-2, -2)
Find the gradient of
Find the gradient of Find the gradient of
the line EF
the line AB the line CD
BAP – 1008HF Gradient & Length Game

3. Find the gradient Find the gradient Find the gradient
of the line between of the line between of the line between
this pair of this pair of this pair of
coordinates coordinates coordinates
(5, -1) and (3, 5) (-5, 14 ) and (1, (-2, 7 ) and (0,
2) 15)
Find the gradient Find the gradient Find the gradient
of the line between of the line between of the line between
this pair of this pair of this pair of
coordinates coordinates coordinates
(4, -4) and (9, 1) (-1, 8) and (1, 2) (7, -3) and (11,
17)
F(-1, y)
B(3, y)
C(0, 4) E(-5, 1)
A(0, -2)
D(x, 1)
)
The gradient of the line
The gradient of the line
is 3, what is the value of The gradient of the line
is 0.5, what is the value
y-coordinate at B? is –1, what is the value of
of the x–coordinate
the x-coordinate at D?
at F?
BAP – 1008HF Gradient & Length Game