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.

Answer 1

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