Question

triangle ABC has been rotated 90° to create triangle DEF. Using the image below, prove that perpendicular lines have opposite and reciprocal slopes.

Answer 1

@phi @ganeshie8 @.Sam.

Answer 2

start by finding the slope of BC

Answer 3

How do I do that?

Answer 4

use slope formula

Answer 5

look at the given diagram,
can u tell the coordinates of B and C ?

Answer 6

B = (?, ?)
C = (?, ?)

Answer 7

B = (4, 5)
C = (1, 1)

Answer 8

Excellent !

Answer 9

next, find the slope of BC using slope formula :

slope = \(\dfrac{y_2 - y_1}{x_2-x_1}\)

Answer 10

B = (4, 5)
x1 y1

C = (1, 1)
x2 y2

Answer 11

slope of BC = \(\dfrac{1-5}{1-4} = \dfrac{-4}{-3} = \dfrac{4}{3}\)

Answer 12

After 90 degree rotation, this BC has moved to EF,
find the slope of EF also same way as above^

Answer 13

first get the coordinates of E and F

Answer 14

E = (-5, 4)
F = (-1, 1)

Slope of EF = \[\frac{ 1 - 4 }{ -5 - -1} = \frac{ -3 }{ -4 }\]

Answer 15

small mistake, let me correct

Answer 16

E = (-5, 4)
x1 y1

F = (-1, 1)
x2 y2

Answer 17

slope of EF = \(\dfrac{1-4}{-1 --5} = \dfrac{-3}{-1+5} = \dfrac{-3}{4}\)

Answer 18

compare this slope with the earlier slope of BC

Answer 19

aren't they reciprocals wid opposite signs ?

Answer 20

I don't understand how they're reciprocals if they have negative numbers.

Answer 21

slope of BC = \(\dfrac{4}{3}\)


slope of EF = \(\dfrac{-3}{4}\)

Answer 22

stare at both of them

Answer 23

you can get one from the other by :
1) taking reciprocal, and
2) flipping the sign

Answer 24

I understand they're recipricoles, but the -3 isn't the same in the BC

Answer 25

thats the reason we call them reciprocals wid opposite signs

Answer 26

Okay, I understand. Thank you.

Answer 27

actually we call them "negative reciprocals" or "opposite reciprocals"

Answer 28

http://www.mathwords.com/n/negative_reciprocal.htm