need coordinate geomertry help please. (1 Viewer)

[Riot09]

the above statement sums it up.(please include working out-since i want learn how to do it), thank you.

in this topic i get the year 9 and 10 stuff since we did it already but the new things i usually decipher the question incorrectly or get the wrong answer since the working out is very thorough.And since maths is my weakest subject even though i havent failed any exams yet.for me for the h.w questions its really hard to find examples or the hard or application questions,so i end up needing help.

so any way these are the homework questions im stuck on and the reasons are stated above if you read this and i thank u for doing so.I dont expect the b.o.s community or you to do all the questions on my "rap sheet"(and u should rightly should) but any help would be very appreciated.

Plus theres this quiz our teacher gives that has like the hardest question anyone can think of and i got 4/5 for the previous one for this topic but the one she gave us a few days ago i cant even do it.

b.t.y these questions are from the math textbook "maths in focus"(3unit-green)

7.7 no.9

find the eqn of the st.line through (-2,0) that passes through the intersection of the lines:

3x+4y-7=0 and 3x-2y-1=0 (the ans is 7x+6y-24=o)

7.8 no.3,4,5

3: a triangle is formed by 3 st.lines with eqn's 2x-y+1=0,2x+y-9=0 and 2x-5y-3=0.find the coordiates of the verticies. (the ans are: (2,5) (4,1) and (-1,1)

4:show the lines x-5y-17=0,3x-2y-12=0 and 5x+y-7=o are cocurret.(the ans is:all lines intersect at (2,-3),.

5:show that the lines x+4y+5=0,3x-7y+15=0,3x-7y+15=0,2x-y+10=0 and 6x+5y+30=o are concurrent.(the ans: is all lines meet at (-5,0)

7.9 no:14,15 and 16

no.14:find the eqn of the st.line with gradient 2 that passes through the intersection of the lines 5x-2y-3=0 and 7x-3y-4=0. (the ans is:2x-y-1=0)

no.15:find the eqn of the st.line parallel to the line 3x-y-7=0 that pasess through the intersectio of the lines 3x-2y-10=0 and 4x+y-17=0.(the ans is:3x-y-11=0

no.16:find the eqn of the st.line perpendicular to the line:x+5y-1=0 that passes through the intersection of lines 3x-5y-3=0 and 2x+3y+17=0.

7.10 no.5,8,11 and 13.

no.5:show that points a(3,-5) and b(-1,4)lie on opposite sides of 2x-y+3=0.(the ans is:a:d positive and b:d is negative-what does that mean?)

no.8:the perpendicular distance between the pt. (x,-1) ad the line 3x-4y+7=0 is 8units.find the two possible values of x.

no.11: prove that the line 3x-4y+25=0 is a tangent to the circle with centre the origin and radius 5units.(show that the distance between (0,0) and the line is 5.

no.13:the sides of a triangle are formed by the lines with eqns 2x-y-7=0,3x-4=0.
find the vertices. (the ans are:coordinates (3,-1),(3 and a quarter and 1/7),(-2,2)

and find the exact length of all the altitudes of the triangle.(for this the ans are:2root 10 over 5,13root5 over 5 and 26root34 over 119.

 

[ohexploitable]

7.7: Find the general equation of the line through the intersection (l₁+kl₂=0), substitute (-2,0), solve for k, substitute the value of k, simplify.

 

[ohexploitable]

7.8 no. 3: Draw the triangle, solve simultaneously.

 

[ohexploitable]

7.8 no.4: Choose two lines and find the general equation of the line through the intersection (l₁+kl₂=0), show that the third line satisfies it.

 

[ohexploitable]

7.8 no. 5: As above.

 

[ohexploitable]

7.9 no. 14: Find the general equation of the line through the intersection (l₁+kl₂=0), find the gradient in terms of k, equate with m=2, solve for k, substitute the value of k, simplify.

 

[ohexploitable]

7.9 no. 15: As above.

 

[ohexploitable]

7.9 no. 16: As above, note: for perpendicular lines, the products of the gradients is -1.

 

[ohexploitable]

7.10 no. 5: The line 2x-y+3=0 separates the cartesian plane into two regions, 2x-y+3<0 and 2x-y+3>0, substitute the points to show they lie on different regions.

 

[ohexploitable]

7.10 no. 8: Use the perpendicular distance formula, substitute known values, solve for x.

 

[ohexploitable]

7.10 no. 11: Use the perpendicular distance formula to show the distance from (0,0) to 3x-4y+25=0 is equal to the radius and hence, is a tangent since it is perpendicular to the radius and touches the circle once.

 

[ohexploitable]

7.10 no. 13: Triangles have three sides, you only posted two equations, but to solve see my solution to 7.8 no. 3. For the second part use the perpendicular distance formula with the vertices and opposite sides.

 

[ohexploitable]

That was really good for my post count! hehe

If you want full answers or more explanation just ask.

 

[thongetsu]

Spammer. Reported.

 

[absolute genius]

find the eqn of the st.line through (-2,0) that passes through the intersection of the lines:

3x+4y-7=0 and 3x-2y-1=0

use the formula they give you in the text book:

1) so you label the coefficients in both of the equations as (A-1) and so on:

3x+4y-7=0 3x-2y-1=0

For this equation: For this equation:

A (1)x = 3 A (2)x = 3
B (1)y = 4 B (2)y = -2
C (1) = -7 C (2) = -1

Now you sub into the formula and you get:

(3x+4y-7) + K (3x-2y-1) = 0

And now since the question has given you the point through which the line passes (-2,0) you simply sub it into your formula

So your x-value is -2
And your y-value is 0

(3(-2) +4(0)-7)+ K (3(-2)-2(0)-1) = 0

And now simplify further:

(-6+0-7) + K (-6-0-1) = 0

-13+ K (-7) = 0

-13-7k = 0

-7k = 13

Therefore: K = -13/7

Now you simply sub the K-value (which we found to be -13/7) back into the formula in which (x) and (y) were unknown. I.e.: (3x+4y-7) + K (3x-2y-1) = 0

We get:

(3x+4y-7) - 13/7 (3x-2y-1) = 0

Now since we don’t like fractions, we get rid of the denominator (7) by multiplying everything by 7

We get:

7(3x+4y-7) -13(3x-2y-1) = 0

Now we simply expand the brackets:

21x-28y+49-39x+26y+13=0

Simplify: -18x+54y-36=0
Divide everything by 9, since it a common factor:

-2x-6y+4=0

2x+6y-4=0 (I just moved everything over to make the x positive)

 

[hscishard]

Everyone uses the k method. Lol. I didn't learn it because I didn't want to remember it.

Lol at exploitable.

 

[random-1005]

the above statement sums it up.(please include working out-since i want learn how to do it), thank you.

in this topic i get the year 9 and 10 stuff since we did it already but the new things i usually decipher the question incorrectly or get the wrong answer since the working out is very thorough.And since maths is my weakest subject even though i havent failed any exams yet.for me for the h.w questions its really hard to find examples or the hard or application questions,so i end up needing help.

so any way these are the homework questions im stuck on and the reasons are stated above if you read this and i thank u for doing so.I dont expect the b.o.s community or you to do all the questions on my "rap sheet"(and u should rightly should) but any help would be very appreciated.

Plus theres this quiz our teacher gives that has like the hardest question anyone can think of and i got 4/5 for the previous one for this topic but the one she gave us a few days ago i cant even do it.

b.t.y these questions are from the math textbook "maths in focus"(3unit-green)

7.7 no.9

find the eqn of the st.line through (-2,0) that passes through the intersection of the lines:

3x+4y-7=0 and 3x-2y-1=0 (the ans is 7x+6y-24=o)

7.8 no.3,4,5

3: a triangle is formed by 3 st.lines with eqn's 2x-y+1=0,2x+y-9=0 and 2x-5y-3=0.find the coordiates of the verticies. (the ans are: (2,5) (4,1) and (-1,1)

4:show the lines x-5y-17=0,3x-2y-12=0 and 5x+y-7=o are cocurret.(the ans is:all lines intersect at (2,-3),.

5:show that the lines x+4y+5=0,3x-7y+15=0,3x-7y+15=0,2x-y+10=0 and 6x+5y+30=o are concurrent.(the ans: is all lines meet at (-5,0)

7.9 no:14,15 and 16

no.14:find the eqn of the st.line with gradient 2 that passes through the intersection of the lines 5x-2y-3=0 and 7x-3y-4=0. (the ans is:2x-y-1=0)

no.15:find the eqn of the st.line parallel to the line 3x-y-7=0 that pasess through the intersectio of the lines 3x-2y-10=0 and 4x+y-17=0.(the ans is:3x-y-11=0

no.16:find the eqn of the st.line perpendicular to the line:x+5y-1=0 that passes through the intersection of lines 3x-5y-3=0 and 2x+3y+17=0.

7.10 no.5,8,11 and 13.

no.5:show that points a(3,-5) and b(-1,4)lie on opposite sides of 2x-y+3=0.(the ans is:a:d positive and b:d is negative-what does that mean?)

no.8:the perpendicular distance between the pt. (x,-1) ad the line 3x-4y+7=0 is 8units.find the two possible values of x.

no.11: prove that the line 3x-4y+25=0 is a tangent to the circle with centre the origin and radius 5units.(show that the distance between (0,0) and the line is 5.

no.13:the sides of a triangle are formed by the lines with eqns 2x-y-7=0,3x-4=0.
find the vertices. (the ans are:coordinates (3,-1),(3 and a quarter and 1/7),(-2,2)

and find the exact length of all the altitudes of the triangle.(for this the ans are:2root 10 over 5,13root5 over 5 and 26root34 over 119.

its just simultaneous eqns, thats all it is, no need to do all of them

 

[random-1005]

Everyone uses the k method. Lol. I didn't learn it because I didn't want to remember it.

Lol at exploitable.

thats the good way to do it, you can just solve simultaneously to point the intersection and then you have two points so you can find m and do y-y1=m(x-x1)

the k method is a waste of time and you are going to make mistakes, memorise the important stuff ( e.g. perpendicluar distance) but most of the stuff can be derived from first principles,