geometry question

[skawal]

Q.a line that pass through three points (a,0), (0,a) and (-3,-3),

col A(a)
col B (-5)

SPOILER: B

my approach was

the slope of the line passing through points (-3,-3),(a,0) and the slope of the line passing through points (-3,-3),(0,a) is equal

so, [0-(-3)]/[a-(-3)]=[a-(-3)]/[0-(-3)]
or,9=(a+3)^2
or,a(a+6)=0
0r, a=0,a=-6
since a=-6 so col B is greater.but i am confused about a=0.in this case my assumptiom is if a=0 the line goes through (0,0),(0,0) and (-3,-3).it is impossible.

is my approach correct?

[hilldog]

Q.a line that pass through three points (a,0), (0,a) and (-3,-3),

col A(a)
col B (-5)

SPOILER: B

my approach was

the slope of the line passing through points (-3,-3),(a,0) and the slope of the line passing through points (-3,-3),(0,a) is equal

so, [0-(-3)]/[a-(-3)]=[a-(-3)]/[0-(-3)]
or,9=(a+3)^2
or,a(a+6)=0
0r, a=0,a=-6
since a=-6 so col B is greater.but i am confused about a=0.in this case my assumptiom is if a=0 the line goes through (0,0),(0,0) and (-3,-3).it is impossible.

is my approach correct?

it intersect x axis at length a, & y axis also a.

so, x/a+y/a=1
x+y=a [equation of that line]

it goes through (-3, -3)

-3-3 = a
a = -6 [so, ans is B]

equation of that line, x+y+6=0;

[skawal]

thanx hilldog for a nice approach.but why you dont make any comment regarding my approach? am i wrong?

[mickgreen58]

The only portion of Hilldog's solution I am confused by is how he generated the equation:

x/a + y/a = 1

[shahadatme]

The only portion of Hilldog's solution I am confused by is how he generated the equation:

x/a + y/a = 1

mickgreen58: The equation of line which cuts the the both axis is
x/a+y/b=1
where, a= the x intercept of the line
b= the y intercept of the line
This is an universal formula for an equation of a line which cuts both axis.

[mickgreen58]

mickgreen58: The equation of line which cuts the the both axis is
x/a+y/b=1
where, a= the x intercept of the line
b= the y intercept of the line
This is an universal formula for an equation of a line which cuts both axis.

Thanks for the information. Of all the equations I have been studying for Coordinate Geometry, I have not seen this one.

[shahadatme]

Q.a line that pass through three points (a,0), (0,a) and (-3,-3),

col A(a)
col B (-5)

SPOILER: B

my approach was

the slope of the line passing through points (-3,-3),(a,0) and the slope of the line passing through points (-3,-3),(0,a) is equal

so, [0-(-3)]/[a-(-3)]=[a-(-3)]/[0-(-3)]
or,9=(a+3)^2
or,a(a+6)=0
0r, a=0,a=-6
since a=-6 so col B is greater.but i am confused about a=0.in this case my assumptiom is if a=0 the line goes through (0,0),(0,0) and (-3,-3).it is impossible.

is my approach correct?

skawal: I think the following approach will provide the answer of your quest.

you know that the equation of a line which has an intercept 'C' is
y=mx+c------------[1]

eqn [1] passes through the points (a,0), (0,a) and (-3,-3)

so, 0=am+c---------------[2]

a=m*0+c
=>c=a------------------[3]

and, -3=-3m+c-------------[4]

From [2] and [3]
am+a=0
=>a[m+1]=0
Since, a/=0 , so m+1=0 [Got the ans of your quest]
=> m=-1
from [4] c=-6
from [3] c=a=-6

So the ans is B

[mickgreen58]

Thanks, I understand this question. For a good resource for understanding this problem, check this site out:

link