9.03 Midpoints
For the segment with endpoints, A \left(x_1,y_1 \right) and B \left(x_2,y_2\right) state the formula for the midpoint, M, of \overline{AB}.
Consider the two points A and B with their midpoint M plotted on the coordinate plane. For each pair of coordinates, find their midpoint M:
A \left(5, - 6 \right) and B \left(5, 2\right)
A \left(6, 5\right) and B \left(14, 7\right)
For each of the following, find the coordinates of M, the midpoint of \overline{AB}:
A \left(5, 4\right) and B \left(5, 10\right)
A \left(-9, -8\right) and B \left(-2, -8\right)
A \left(0, 0\right) and B \left(0, 16\right)
A \left(0, 0\right) and B \left(-5,0\right)
A \left(0, 0\right) and B \left(10, 8\right)
A \left(0, 0\right) and B \left(-12, 4\right)
For each of the following, find the coordinates of M, the midpoint of \overline{AB}:
A \left( - 8 , - 4 \right) and B \left(2, 8\right)
A \left( - 7 , 3\right) and B \left(1, - 7 \right)
For each pair of points A and B given:
Find the coordinates of the midpoint M.
Plot \overline{AB} and the point M on a coordinate plane.
A \left( - 9 , 1\right) and B \left(5, - 7 \right)
A \left( -1 , -4 \right) and B \left( 8, -7\right)
A \left(-7, 3 \right) and B \left( - 4 , -7\right)
A \left( - \dfrac{3}{4} , - 6 \right) and B \left( \dfrac{11}{4}, 4 \right)
A \left(\dfrac{1}{2}, - 2 \right) and B \left( - 2 , \dfrac{7}{2}\right)
Find the midpoint of A \left( 2 m, 5 n\right) and B \left( 6 m, n\right).
Given that M is the midpoint of A and B, find the coordinates of A in the following given points:
B \left(9, 6\right) and M \left(7, 6\right)
B \left(16, 7\right) and M \left(10, 2\right)
B \left(8,8\right) is M \left(-2,0 \right)
B \left(2, - 9 \right) and M \left(-1, - 7 \right)
The graph shows the annual net profit (in millions) of a company over the last few years. It shows that its profit has been growing approximately linearly from \$19 million in 2008 to \$39 million in 2014.
By finding the midpoint of the line segment, determine the company's net profit in 2011.
Lines of latitude and longitude measure position on the Earth’s surface and work like coordinates. The first coordinate represents how far above or below the equator you are, and the second coordinate measures how far from Greenwich Mean Time you are.
A plane starts its flight at \left( 20 \degree \text{N}, 62 \degree \text{E} \right). It is bound for its destination at \left(52 \degree \text{N}, 146 \degree \text{E} \right). Assuming the plane flies directly to its destination, find its position half way through the flight.
The points P,Q,R,S and T are collinear, and PQ=QR=RS=ST.
Find the points Q, R and S given P \left( - 4 , - 2 \right) and T \left( - 12 , 10\right).
M \left( 4 p + 2, 5 q - 3\right) is the midpoint of S \left(20, - 12 \right) and T \left( - 18 , 6\right).
Find the value of p.
Find the value of q.
Point C \left(1,1\right) is one quarter of the way from the point A \left(-3,-2\right) to point B. Find the coordinates of point B. Explain your process.
M is the midpoint of \overline{AB}. The coordinates of point A are \left(x_A,12\right), the coordinates of point M are \left(x_M, 4\right), and the coordinates of B are \left(6, -4\right).
Given that AB=20, find the x-coordinates of A and M.