Question

The co-ordinates of two points P and Q are (2,6) and (-3, 5) respectively. Find:
(i) the gradient of PQ;
(ii) the equation of PQ;
(iii) the co-ordinates of the point where PQ intersects the x-axis.​

Answer 1

Answer:

Answered in attachments...

By,

Avni Dontulwar

Answer 2

Given:

The co-ordinates of two points P and Q are (2,6) and (-3, 5) respectively.

To Find:

(i) the gradient of PQ;

(ii) the equation of PQ;

(iii) the co-ordinates of the point where PQ intersects the x-axis.

Solution:

(i) Gradient of PQ

P(2,6) Q(-3,5)

Gradient of PQ = 5-6/-3-2 = -1/-5 = 1/5

Gradient of PQ = 1/5

(ii) Equation of PQ

As we know equation of line is given by

=> ( y - y1 ) = m( x - x1 )

=> ( y - 6 ) = 1/5 ( x - 2 )

=> 5( y - 6) = ( x -2 )

=> 5y - 30 = x - 2

=> x - 5y + 28 = 0

(iii) Co-ordinates of the point where PQ intersects the x-axis

Let line PQ in intersects the x-axis at point (x,0)

Putting the values of this point in equation of line.

x - 5(0) + 28 = 0

x + 28 = 0

x = -28

Hence , the co-ordinates of the point where PQ intersects the x-axis are A (−28, 0)