Coordinate Geometry BARNES

Question 1

For two coordinates (x1, y1) and (x2, y2), the distance between them is

Answer 1

d = √ (x2-x1)^2 + (y2-y1)^2

Question 2

Find all points of form (a, a) which are 5 units distant from the point (0, 1)

Answer 2

(4,4) or (-3,-3)

Question 3

For two coordinates (x1, y1) and (x2, y2), the midpoint is

Answer 3

( x1+x2 / 2 ) , ( y1+y2 / 2 )

Question 4

the set of points (x, y) are defined by the property that the distance to (0, 1)
equals y. Find the equation connecting x and y.

Answer 4

y = x^2 + 1 / 2

Question 5

The line through points (x1, y1) and (x2, y2) has a gradient equal to

Answer 5

m = y2-y1 / x2-x1

Question 6

the line through points (x1, y1) and (x2, y2) has an equation of

Answer 6

y - y1 = m (x - x1)
y = mx + c
or ay + bx + d = 0

Question 7

Find the x- and y-intercept of the line through points (2, -3) and (-1, 4)

Answer 7

x = 5/7
y = 5/3

Question 8

two lines are perpendicular if their gradients obey

Answer 8

m1m2 = -1

Question 9

A perpendicular bisector of segment AB is

Answer 9

perpendicular to AB, and passes through the midpoint of AB

Question 10

Find the equation of the perpendicular bisector of the line segment joining
(4, -3) and (1, 5). Give your answer in the form ax + by = c.

Answer 10

16y - 6x = 1