NBT NBT Mathematics: Analytical Geometry

Question 1

What is the distance between the points (-2, 3) and (4, -5)?

Accepted Answer

10

Answer

d = √((4+2)² + (-5-3)²) = √(36+64) = √100 = 10.

Question 2

What is the midpoint of the segment joining (3, -7) and (-5, 1)?

Accepted Answer

(-1, -3)

Answer

Midpoint = ((3−5)/2, (−7+1)/2) = (−1, −3).

Question 3

M(2, 5) is the midpoint of AB, where A is (-1, 8). What are the coordinates of B?

Accepted Answer

(5, 2)

Answer

B = (2·2 − (−1), 2·5 − 8) = (5, 2).

Question 4

What is the slope of a line perpendicular to 3x − 4y = 12?

Accepted Answer

-4/3

Answer

The given line has slope 3/4, so a perpendicular line has slope −4/3.

Question 5

Which equation describes the line through (1, 2) parallel to y = −2x + 7?

Accepted Answer

y = −2x + 4

Answer

Parallel lines share slope −2; substituting (1, 2) gives c = 4.

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