The co-ordinates of two points P and Q are (2, 6) and (-3, 5) respectively. Find : (i) the gradient of PQ; (ii) the equation of PQ; (iii) the co-ordinates of the point where PQ intersects the x-axis.

(i) By formula, Slope = Substituting values we get, Hence, gradient of slope PQ = . (ii) By point slope form, Equation : y - y 1 = m(x - x 1 ) ⇒ y - 6 = (x - 2) ⇒ 5(y - 6) = x - 2 ⇒ 5y - 30 = x - 2 ⇒ 5y = x - 2 + 30 ⇒ 5y = x + 28 Hence, equation of PQ is 5y = x + 28. (iii) The point where PQ intersects x-axis, there y co-ordinate = 0. Substituting y = 0 in equation of PQ we get, ⇒ 5 × 0 = x + 28 ⇒ 0 = x + 28 ⇒ x = -28. Point = (x, y) = (-28, 0). Hence, co-ordinates of the point where PQ intersects the x-axis = (-28, 0).

Find the equation of a line which passes through (5, 4) and makes an angle of 60° with the positive direction of the x-axis.

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Find the equation of a line passing through :
(i) (0, 1) and (1, 2)
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(i) the equation of AB;
(ii) the co-ordinates of the point where the line AB intersects the y-axis.

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The figure given alongside shows two straight lines AB and CD intersecting each other at point P (3, 4). Find the equations of AB and CD.

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Mathematics

The co-ordinates of two points P and Q are (2, 6) and (-3, 5) respectively. Find :
(i) the gradient of PQ;
(ii) the equation of PQ;
(iii) the co-ordinates of the point where PQ intersects the x-axis.

Straight Line Eq

Related Questions

Find the equation of a line which passes through (5, 4) and makes an angle of 60° with the positive direction of the x-axis.

Find the equation of a line passing through :
(i) (0, 1) and (1, 2)
(ii) (-1, -4) and (3, 0)

The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find :
(i) the equation of AB;
(ii) the co-ordinates of the point where the line AB intersects the y-axis.

The figure given alongside shows two straight lines AB and CD intersecting each other at point P (3, 4). Find the equations of AB and CD.

Mathematics

The co-ordinates of two points P and Q are (2, 6) and (-3, 5) respectively. Find :(i) the gradient of PQ;(ii) the equation of PQ;(iii) the co-ordinates of the point where PQ intersects the x-axis.

Straight Line Eq

Related Questions

Find the equation of a line which passes through (5, 4) and makes an angle of 60° with the positive direction of the x-axis.

Find the equation of a line passing through :(i) (0, 1) and (1, 2)(ii) (-1, -4) and (3, 0)

The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find :(i) the equation of AB;(ii) the co-ordinates of the point where the line AB intersects the y-axis.

The figure given alongside shows two straight lines AB and CD intersecting each other at point P (3, 4). Find the equations of AB and CD.

The co-ordinates of two points P and Q are (2, 6) and (-3, 5) respectively. Find :
(i) the gradient of PQ;
(ii) the equation of PQ;
(iii) the co-ordinates of the point where PQ intersects the x-axis.

Find the equation of a line passing through :
(i) (0, 1) and (1, 2)
(ii) (-1, -4) and (3, 0)

The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find :
(i) the equation of AB;
(ii) the co-ordinates of the point where the line AB intersects the y-axis.