Straight Line

Question 1

distance formula

Answer 1

d=square root or (x2-x1)^2+(y2-y1)^2

Question 2

midpoint formula

Answer 2

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

Question 3

gradient formulas

Answer 3

1. y2-y1/x2-x1

2. m=tantheta positive direction of x-axis

Question 4

types of gradient

Answer 4

• lines with positive gradients slope up from left to right
• lines with negative gradients slope down from right to left
• lines parallel to x-axis have a gradient of zero
• lines parallel to y-axis have an undefined gradient

Question 5

parallel lines

Answer 5

same gradient

Question 6

collinear

Answer 6

points which lie on the same straight line

• work out mab and mbc –> if same collinear
• must also share a common point

Question 7

perpendicular lines

Answer 7

at right angles with each other

m1xm2=-1

Question 8

equation of a straight line formula

Answer 8

y-b=m(x-a)

y=mx+c

Question 9

general form of equation of straight line

Answer 9

ax+by+c=0

Question 10

lines parallel to axis

Answer 10

• if line is parallel to x-axis y=c

- if line is parallel to y-axis x=k

Question 11

median

Answer 11

line through a vertex and the midpoint of the opposite side

Question 12

process of calculating median

Answer 12

1. calculate midpoint of relevant line
2. calculate gradient of line between midpoint and vertex
3. find equation using gradient and either point

Question 13

altitude

Answer 13

line through a vertex, perpendicular to the opposite side

Question 14

process of calculating altitude

Answer 14

1. calculate gradient of side perpendicular to altitude
2. m1xm2=-1
3. find equation using gradient and point

Question 15

perpendicular bisector

Answer 15

line which cuts through the midpoint of a line segment at right angles

Question 16

process of finding perpendicular bisector

Answer 16

1. calculate midpoint of line segment being bisected
2. calculate gradient of line used in step 1 then find gradient of perpendicular bisector (m1xm2=-1)
3. find equation of perpendicular bisector using point in step 1 and gradient in step 2.

Question 17

intersection of lines

Answer 17

simultaneous equations

Question 18

concurrency

Answer 18

any line are said to be concurrent if there is a point through which they all pass.

Question 19

what is the point of intersection of medians called?

Answer 19

centroid

Question 20

what is the point of intersection of altitudes called?

Answer 20

orthocentre

Question 21

what is the point of intersection of perpendicular bisectors called?

Answer 21

circumcentre

Question 22

what is the point of intersection of angle bisectors called?

Answer 22

incentre

Question 23

gradient of horizontal line

Answer 23

0

Question 24

gradient of vertical line

Answer 24

undefined

Question 25

equation of horizontal line

Answer 25

y=c

Question 26

equation of vertical line

Answer 26

x=k