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Lines Parallel to Coordinate Axes

Given: define...

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Given: define distance between two points P(x1, y1) and (x2, y2) as d(P, Q)= max. {|x2-x1|, |y2-y1|} Suppose that points A and B have coordinates (1,0) and (-1,0) respectively, then for a variable point P on this plane the equation d(P, A) + d(P,B)= 2 represents: A) a line segment joining A and B B) an ellipse with foci at A and B C) region lying inside a square of area 2 D) region inside a semicircle with AB as diameter

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P = (x_{1}, y_{1}) and Q = (x_{2}, y_{2})

d (P, Q)

d (P, Q) = | x_{1} - x_{2} | + | y_{1} - y_{2} |

O = (0, 0)

A = (3, 2)

O

A

P \equiv (x_{1}, y_{1})

Q \equiv (x_{2}, y_{2})

d (P, Q) = | x_{1} - x_{2} | + | y_{1} - y_{2} |

O \equiv (0, 0), A \equiv (2, 3)

C \equiv (4, 3)

x - y

R (x, y)

R

O

A

0 \leq x < 1

0 \leq y < 2

R

The coordinates of the mid-point of the line segment joining two points P(X₁, y₁, z₁) and Q(x₂, y₂, z₂) are:

△ A B C .

△ A B C,

d (P, B C) \leq m i n d (P, A B), d (P, A C),

d (P, B C)

(d (P, B C)

P (x_{1}, y_{1})

Q (x_{2}, y_{2})

\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2} .

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