Find the equation of the line passing through the points P(5, 1) and Q(1, -1). Hence, show that the points P, Q and R(11, 4) are collinear.

The two given points are P(5, 1), Q(1, -1). Slope of the line = So, the equation of PQ is ⇒ y - y 1 = m(x - x 1 ) ⇒ y - 1 = ⇒ 2(y - 1) = x - 5 ⇒ 2y - 2 = x - 5 ⇒ x - 2y - 5 + 2 = 0 ⇒ x - 2y - 3 = 0. Now if point R(11, 4) is collinear to points P and Q then it will satisfy the equation x - 2y - 3 = 0, Putting values in L.H.S of the equation The equation of the line PQ is x - 2y - 3 = 0. Since, L.H.S. = 0 = R.H.S, thus R satisfies the equation. Hence, points P, Q and R are collinear.

Find the intercepts made by the line 2x - 3y + 12 = 0 on the coordinate axes.

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Find the value of 'a' for which the following points A(a, 3), B(2, 1) and C(5, a) are collinear. Hence, find the equation of the line.

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The coordinates of two points E and F are (0, 4) and (3, 7) respectively. Find :
(i) the gradient of EF.
(ii) the equation of EF.
(iii) the coordinates of the point where the line EF intersects the x-axis.

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Mathematics

Find the equation of the line passing through the points P(5, 1) and Q(1, -1). Hence, show that the points P, Q and R(11, 4) are collinear.

Straight Line Eq

Related Questions

Find the intercepts made by the line 2x - 3y + 12 = 0 on the coordinate axes.

Find the value of 'a' for which the following points A(a, 3), B(2, 1) and C(5, a) are collinear. Hence, find the equation of the line.

The coordinates of two points E and F are (0, 4) and (3, 7) respectively. Find :
(i) the gradient of EF.
(ii) the equation of EF.
(iii) the coordinates of the point where the line EF intersects the x-axis.

Mathematics

Find the equation of the line passing through the points P(5, 1) and Q(1, -1). Hence, show that the points P, Q and R(11, 4) are collinear.

Straight Line Eq

Related Questions

Find the intercepts made by the line 2x - 3y + 12 = 0 on the coordinate axes.

Find the value of 'a' for which the following points A(a, 3), B(2, 1) and C(5, a) are collinear. Hence, find the equation of the line.

The coordinates of two points E and F are (0, 4) and (3, 7) respectively. Find :(i) the gradient of EF.(ii) the equation of EF.(iii) the coordinates of the point where the line EF intersects the x-axis.

The coordinates of two points E and F are (0, 4) and (3, 7) respectively. Find :
(i) the gradient of EF.
(ii) the equation of EF.
(iii) the coordinates of the point where the line EF intersects the x-axis.