Graphs, Equations, And Inequalities Worksheets Page 11
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11B11
Appendix B.1
The Cartesian Plane
95.
Physical Education
In a football game, a quarterback
102.
Exploration
A line segment has
x
, y
as one
1
1
throws a pass from the 15-yard line, 10 yards from the
x
, y
endpoint and
as its midpoint. Find the other
m
m
sideline, as shown in the figure. The pass is caught on
x
, y
endpoint
of the line segment in terms of
x
,
y
,
2
2
1
1
the 40-yard line, 45 yards from the same sideline. How
x
,
and
y
.
Use the result to find the coordinates of the
m
m
long is the pass?
endpoint of a line segment when the coordinates of the
other endpoint and midpoint are, respectively,
50
(a)
1,
2 , 4,
1 .
(b)
5, 11 , 2, 4 .
(45, 40)
40
103.
Exploration
Use the Midpoint Formula three times
30
to find the three points that divide the line segment
x
, y
x
, y
joining
and
into four parts. Use the
20
1
1
2
2
result to find the points that divide the line segment
(10, 15)
10
joining the given points into four equal parts.
10
20
30
40
50
(a)
1,
2 , 4,
1
(b)
2,
3 , 0, 0
Distance (in yards)
104.
Think About It
Use the plot of the point
x
y
in the
0,
0
96.
Physical Education
A major league baseball diamond
figure. Match the transformation of the point with the
correct plot. Explain your reasoning. [The plots are
is a square with 90-foot sides. In the figure, home plate
is at the origin and the first base line lies on the positive
labeled (i), (ii), (iii), and (iv).]
x
-axis. The right fielder fields the ball at the point
y
300, 25
. How far does the right fielder have to throw
the ball to get a runner out at home plate? How far
(x
, y
)
does the right fielder have to throw the ball to get a
0
0
x
runner out at third base? (Round your answers to one
decimal place.)
y
y
y
(i)
(ii)
150
(0, 90)
100
x
x
50
(300, 25)
(0, 0)
x
50
100
150
200
250
300
y
y
(iii)
(iv)
Distance (in feet)
Conclusions
x
x
True or False?
In Exercises 97–99, determine whether
the statement is true or false. Justify your answer.
97. The points
8, 4 ,
2, 11 ,
and
5, 1
represent the
vertices of an isosceles triangle.
(a)
x
,
y
(b)
2x
, y
0
0
0
0
1
98. If four points represent the vertices of a polygon, and
(c)
x
,
y
(d)
x
,
y
0
2
0
0
0
the four sides are equal, then the polygon must be a
105.
Proof
Prove that the diagonals of the parallelogram
square.
in the figure intersect at their midpoints.
99. In order to divide a line segment into 16 equal parts,
y
you would have to use the Midpoint Formula 16 times.
100.
Think About It
What is the -coordinate of any point
y
(b, c)
(a + b, c)
on the -axis? What is the -coordinate of any point on
x
x
the -axis?
y
x
Think About It
101.
When plotting points on the
(0, 0)
(a, 0)
rectangular coordinate system, is it true that the scales
on the
and axes must be the same? Explain.
x-
y-
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