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Question
The coordinates of two points P and Q are (0,4) and (3,7) respectively. Find
(i) The gradient of PQ
(ii) the equation of PQ
(iii) the coordinates of the point where the line AB intersects the X-axis.
Solution
Slope of PQ = `(7 - 4)/(3 - 0)` = 1
(i) tan θ = 1
`therefore` Gradient = 1
(ii) Equation of PQ ⇒ `("y" - "y"_1)/("x" - "x"_1)` = slope
`("y" - 7)/("x" - 3)` = 1
⇒ x - 3 = y - 7
⇒ y = x + 4
(iii)
Let A (x,0) divides PQ is the ratio k : 1
Using section formula,
Coordinates of A (x,0) = `((3"k")/("k" + 1), (7"k" + 4)/("k" + 1))`
Equating we get
`(7"k" + 4)/("k" + 1)` = 0
7k + 4 = 0
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