A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects x-axis and y-axis at the points A and B respectively and M is the mid-point of AB. Find :
(i) the equation of the line
(ii) the co-ordinates of A and B
(iii) the co-ordinates of M

Question

A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects x-axis and y-axis at the points A and B respectively and M is the mid-point of AB. Find :
(i) the equation of the line
(ii) the co-ordinates of A and B
(iii) the co-ordinates of M

KnowledgeBoat · Accepted Answer

(i) Given points, P(-1, 4) and Q(5, -2) By point-slope form, Equation of the line PQ, y - y1 = m(x - x1) ⇒ y - 4 = -1[x - (-1)] ⇒ y - 4 = -1[x + 1] ⇒ y - 4 = -x - 1 ⇒ x + y = -1 + 4 ⇒ x + y - 3 = 0. Hence, equation of line is x + y - 3 = 0. (ii) For point A (on x-axis), y = 0. So, putting y = 0 in the equation of PQ, we have ⇒ x + 0 = 3 ⇒ x = 3. ∴ A = (3, 0). For point B (on y-axis), x = 0. So, putting x = 0 in the equation of PQ, we have ⇒ 0 + y = 3 ⇒ y = 3 ∴ B = (0, 3). Hence, co-ordinates of A = (3, 0) and B = (0, 3). (iii) M is the mid-point of AB. ∴ M = = = Hence, mid-point of AB = .

Mathematics

A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects x-axis and y-axis at the points A and B respectively and M is the mid-point of AB. Find :
(i) the equation of the line
(ii) the co-ordinates of A and B
(iii) the co-ordinates of M

Straight Line Eq

Related Questions

Find the gradient and the equation of the line passing through the points:
(i) A(–2, 1) and B(3, –4)
(ii) A(4, –2) and B(2, –3)

A(2, 3) and B(–2, 5) are two given points. Find :
(i) the gradient of AB
(ii) the equation of AB
(iii) the co-ordinates of the point, where AB intersects x-axis.

A straight line passes through the points A(2, –4) and B(5, –2). Find :
(i) the slope of the line AB
(ii) the equation of the line AB
(iii) the value of k, if AB passes through the point P(k + 3, k – 4)

Mathematics

A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects x-axis and y-axis at the points A and B respectively and M is the mid-point of AB. Find :(i) the equation of the line(ii) the co-ordinates of A and B(iii) the co-ordinates of M

Straight Line Eq

Related Questions

Find the gradient and the equation of the line passing through the points:(i) A(–2, 1) and B(3, –4)(ii) A(4, –2) and B(2, –3)

A(2, 3) and B(–2, 5) are two given points. Find :(i) the gradient of AB(ii) the equation of AB(iii) the co-ordinates of the point, where AB intersects x-axis.

A straight line passes through the points A(2, –4) and B(5, –2). Find :(i) the slope of the line AB(ii) the equation of the line AB(iii) the value of k, if AB passes through the point P(k + 3, k – 4)

A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects x-axis and y-axis at the points A and B respectively and M is the mid-point of AB. Find :
(i) the equation of the line
(ii) the co-ordinates of A and B
(iii) the co-ordinates of M

Find the gradient and the equation of the line passing through the points:
(i) A(–2, 1) and B(3, –4)
(ii) A(4, –2) and B(2, –3)

A(2, 3) and B(–2, 5) are two given points. Find :
(i) the gradient of AB
(ii) the equation of AB
(iii) the co-ordinates of the point, where AB intersects x-axis.

A straight line passes through the points A(2, –4) and B(5, –2). Find :
(i) the slope of the line AB
(ii) the equation of the line AB
(iii) the value of k, if AB passes through the point P(k + 3, k – 4)