Question

If
the
line 3x+ 4y- 8=0 is denoted by L,
points (2,-5) (5,2) ​

Answer 1

Step-by-step explanation:

Given that: If the line 3x+ 4y- 8=0 is denoted by L, points (2,-5) (5,2)

To find:

(I)Points lie on L

(II) Points lies on same side of L

(III)Points lies on opposite side of L

(IV) None of these

Solution:

Tip:

1. if L(A) =0 and L(B)=0 then Points lie on L
2. if L(A) =0 and L(B)=0 then Points lie on LIf L(A) >0 and L(B)>0 and If L(A) <0 and L(B)< 0,then Points lies on same side of L
3. if L(A) =0 and L(B)=0 then Points lie on LIf L(A) >0 and L(B)>0 and If L(A) <0 and L(B)< 0,then Points lies on same side of Lif L(A) >0 and L(B)< 0 and If L(A) <0 and L(B)> 0Points lies on opposite side of L

Now put the values of A and B in given line and related with three given theorems/facts

Line:

$3x + 4y - 8 = 0 \\ \\as \: A = (2, - 5) \\ \\ L(A) = 3 \times 2 + 4( - 5) - 8 \\ \\ = 6 - 20 - 8 \\ \\ L(A)= - 22...eq1 \\ \\B = (5,2) \\ \\ L(B) = 3(5) + 4(2) - 8 \\ \\ = 15 + 8 - 8 \\ \\ L(B)= 15...eq2$

It is clear from eq1 and eq2 that fact /theorem 3 is true with the given points, thus both points lies opposite side of L.

Hence Option 3 is correct.

Hope it helps you.

To learn more on brainly:

1)Find the distance of the point p(2,5) from the line 3x+4y+14=0

https://brainly.in/question/14447188

2)If the line 3x + 4y - 8=0is denoted by L, then the points (2,-5).(-5,2)

https://brainly.in/question/29178971

Answer 2

Answer:

Option 3 is correct......