Question

Points A and B are the respective x and y-intercepts of the line y+x-c=0. Given that the length of AB is 4 units, find the positive value of c.

Answer 1

help @shamil98 @hartnn

Answer 2

What is an x intercept pythagoras ?

Answer 3

the place where the line cuts the x-axis.

Answer 4

Right, let us say (a,0) is the x intercept and (0,b) the y intercept
then satisfy both the coordinates on the line x+y-c=0 and also use distance formula between the coordinates.

Answer 5

i don't get it... can you show how do to it? :)

Answer 6

to get intercepts algebraically,
for x intercept, put y = 0
for y intercept, put x=0

Answer 7

once u get 2 intercepts, use the distance formula

Answer 8

I got \[y = -x + c \] and \[x ^{2} + y ^{2}\] = 4

but im not sure how to proceed from here cause there's 3 unknowns and only 2 equations
I take that since A and B are x and y intercepts, AB is a downward sloping line - hence I used pythagoras's theorem to find AB since AB is the hypotenuse.

Answer 9

distance formula is pythagoras theorem?

Answer 10

x intercept ----> y= 0

0+x-c = 0
x=c
so the x intercept is (c,0)
got this ?

Answer 11

yep

Answer 12

similarly find y intercept ?

Answer 13

but wouldn't y intercept be c also?

Answer 14

cause in y=mx +c formula, c is the y intercept

Answer 15

then x = y?

Answer 16

yes
so the y intercept = 0,c
now u have 2 points

c,0 and 0,c
apply distance formula

Answer 17

Distance between points (x1,y1) and (x2,y2) is
\(\huge d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)

Answer 18

\(\huge 4=\sqrt{(c-0)^2+(0-c)^2}\)

find c from here

Answer 19

so c is square root 2?

Answer 20

16 = 2c^2
c^2 = 8
how square root 2 ?
wouldn't it be 2 root 2 ?

Answer 21

oh ya forgot to square the 4

Answer 22

thanks so much :D

Answer 23

you're welcome ^_^