Mathematics
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.
Straight Line Eq
3 Likes
Answer
(i) Given points, A(2, 3) and B(–2, 5)
Hence, slope = .
(ii) By point-slope form,
Equation of the line AB, y - y1 = m(x - x1)
⇒ y - 3 = (x - 2)
⇒ 2(y - 3) = -1(x - 2)
⇒ 2y - 6 = -x + 2
⇒ x + 2y = 6 + 2
⇒ x + 2y = 8.
Hence, equation of line is x + 2y = 8.
(iii) The line intersects the x-axis when y = 0. Substituting y = 0 into the equation of the line, x + 2y = 8, we get :
⇒ x + 2(0) = 8
⇒ x = 8
Hence, coordinates of the point where AB intersects the x-axis are (8, 0).
Answered By
3 Likes
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 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
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)
If A(3, 4), B(7, –2) and C(–2, –1) are the vertices of a ΔABC, write down the equation of the median through the vertex C.