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 = ${\displaystyle \frac{7-4}{3-0}}$ = 1

(i) tan θ = 1

${\displaystyle \therefore }$ Gradient = 1

(ii) Equation of PQ ⇒ ${\displaystyle \frac{\text{y}-{\text{y}}_1}{\text{x}-{\text{x}}_1}}$ = slope

    ${\displaystyle \frac{\text{y}-7}{\text{x}-3}}$ = 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) = ${\displaystyle (\frac{3\text{k}}{\text{k}+1},\frac{7\text{k}+4}{\text{k}+1})}$ 

Equating we get

${\displaystyle \frac{7\text{k}+4}{\text{k}+1}}$ = 0

7k + 4 = 0