Find, which of the following points lie on the line x – 2y + 5 = 0(i

1.	Find, which of the following points lie on the line x – 2y + 5 = 0(i) (1, 3) (ii) (0, 5) (iii) (-5, 0) (iv) (5, 5) (v) (2, -1.5) (vi) (-2, -1.5)
Answer» The given line is x − 2y + 5 = 0. (i) Substituting x = 1 and y = 3 in the given equation, we have: L.H.S. = 1 – 2 x 3 + 5 = 1 − 6 + 5 = 6 − 6 = 0 = R.H.S. Thus, the point (1, 3) lies on the given line. (ii) Substituting x = 0 and y = 5 in the given equation, we have: L.H.S. = 0 − 2 x 5 + 5 = −10 + 5 = −5 ≠ R.H.S. Thus, the point (0, 5) does not lie on the given line. (iii) Substituting x = −5 and y = 0 in the given equation, we have: L.H.S. = −5 − 2 x 0 + 5 = −5 − 0 + 5 = 5 − 5 = 0 = R.H.S. Thus, the point (−5, 0) lie on the given line. (iv) Substituting x = 5 and y = 5 in the given equation, we have: L.H.S. = 5 − 2 x 5 + 5 = 5 − 10 + 5 = 10 − 10 = 0 = R.H.S. Thus, the point (5, 5) lies on the given line. (v) Substituting x = 2 and y = −1.5 in the given equation, we have: L.H.S. = 2 − 2 x (−1.5) + 5 = 2 + 3 + 5 = 10 ≠ R.H.S. Thus, the point (2, −1.5) does not lie on the given line. (vi) Substituting x = −2 and y = −1.5 in the given equation, we have: L.H.S. = −2 − 2 x (−1.5) + 5 = −2 + 3 + 5 = 6 ≠ R.H.S. Thus, the point (-2, -1.5) does not lie on the given line.

Find, which of the following points lie on the line x – 2y + 5 = 0(i) (1, 3) (ii) (0, 5) (iii) (-5, 0) (iv) (5, 5) (v) (2, -1.5) (vi) (-2, -1.5)

Answer»

The given line is x − 2y + 5 = 0.

(i) Substituting x = 1 and y = 3 in the given equation, we have:

L.H.S. = 1 – 2 x 3 + 5

= 1 − 6 + 5

= 6 − 6

= 0

= R.H.S.

Thus, the point (1, 3) lies on the given line.

(ii) Substituting x = 0 and y = 5 in the given equation, we have:

L.H.S. = 0 − 2 x 5 + 5

= −10 + 5

= −5 ≠ R.H.S.

Thus, the point (0, 5) does not lie on the given line.

(iii) Substituting x = −5 and y = 0 in the given equation, we have:

L.H.S. = −5 − 2 x 0 + 5

= −5 − 0 + 5

= 5 − 5

= 0 = R.H.S.

Thus, the point (−5, 0) lie on the given line.

(iv) Substituting x = 5 and y = 5 in the given equation, we have:

L.H.S. = 5 − 2 x 5 + 5

= 5 − 10 + 5

= 10 − 10

= 0 = R.H.S.

Thus, the point (5, 5) lies on the given line.

(v) Substituting x = 2 and y = −1.5 in the given equation, we have:

L.H.S. = 2 − 2 x (−1.5) + 5

= 2 + 3 + 5

= 10 ≠ R.H.S.

Thus, the point (2, −1.5) does not lie on the given line.

(vi) Substituting x = −2 and y = −1.5 in the given equation, we have:

L.H.S. = −2 − 2 x (−1.5) + 5

= −2 + 3 + 5

= 6 ≠ R.H.S.

Thus, the point (-2, -1.5) does not lie on the given line.