The ordinate of a point lying on the line joining the points (6, 4) and (7, -5) is -23. Find the co-ordinates of that point.

Let point A = (6, 4) and B = (7, -5). Let the point P be (a, -23). By formula, Slope = Slope of AB = = -9. By point-slope form, ⇒ y - y 1 = m(x - x 1 ) ⇒ y - 4 = -9(x - 6) ⇒ y - 4 = -9x + 54 ⇒ 9x + y = 54 + 4 ⇒ 9x + y = 58. Since, P lies on AB so it will satisfy the equation. Substituting values of P in equation we get, ⇒ 9(a) + (-23) = 58 ⇒ 9a - 23 = 58 ⇒ 9a = 58 + 23 ⇒ 9a = 81 ⇒ a = ⇒ a = 9. ∴ P = (a, -23) = (9, -23). Hence, co-ordinates of the required point are (9, -23).

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Point A and B have co-ordinates (7, -3) and (1, 9) respectively. Find :
(i) the slope of AB.
(ii) the equation of perpendicular bisector of the line segment AB.
(iii) the value of 'p' if (-2, p) lies on it.

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A and B are the two points on the x-axis and y-axis respectively. P(2, -3) is the mid-point of AB.
Find :
(i) the coordinates of A and B.
(ii) the slope of the line AB.
(iii) the equation of the line AB.

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Mathematics

The ordinate of a point lying on the line joining the points (6, 4) and (7, -5) is -23. Find the co-ordinates of that point.

Straight Line Eq

Related Questions

Point A and B have co-ordinates (7, -3) and (1, 9) respectively. Find :
(i) the slope of AB.
(ii) the equation of perpendicular bisector of the line segment AB.
(iii) the value of 'p' if (-2, p) lies on it.

A and B are the two points on the x-axis and y-axis respectively. P(2, -3) is the mid-point of AB.
Find :
(i) the coordinates of A and B.
(ii) the slope of the line AB.
(iii) the equation of the line AB.

Mathematics

The ordinate of a point lying on the line joining the points (6, 4) and (7, -5) is -23. Find the co-ordinates of that point.

Straight Line Eq

Related Questions

Point A and B have co-ordinates (7, -3) and (1, 9) respectively. Find :(i) the slope of AB.(ii) the equation of perpendicular bisector of the line segment AB.(iii) the value of 'p' if (-2, p) lies on it.

A and B are the two points on the x-axis and y-axis respectively. P(2, -3) is the mid-point of AB.Find :(i) the coordinates of A and B.(ii) the slope of the line AB.(iii) the equation of the line AB.

Point A and B have co-ordinates (7, -3) and (1, 9) respectively. Find :
(i) the slope of AB.
(ii) the equation of perpendicular bisector of the line segment AB.
(iii) the value of 'p' if (-2, p) lies on it.

A and B are the two points on the x-axis and y-axis respectively. P(2, -3) is the mid-point of AB.
Find :
(i) the coordinates of A and B.
(ii) the slope of the line AB.
(iii) the equation of the line AB.