Question

1. The coordinates of P and Q are (-4,-7) and (6,3) respectively, X is the mid-point of PQ.
Calculate
a. the length of PQ
b. the gradient of PQ
c. the co-ordinates of X
d. the intercept on the y axis
e. the equation of the straight line which passes through the points P and Q.
f. State the gradient of the perpendicular bisector of PQ.
g. Given the fact that the perpendicular bisector passes through the Midpoint X, Calculate the equation of the Perpendicular bisector of PQ

Answer 1

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Answer 2

Given:    The coordinates of P and Q are (-4,-7) and (6,3) respectively, X is the mid-point of PQ.

To Find :  

a. the length of PQ

b. the gradient of PQ

c. the co-ordinates of X

d. the intercept on the y axis

e. the equation of the straight line which passes through the points P and Q.

f. State the gradient of the perpendicular bisector of PQ.

g. Given the fact that the perpendicular bisector passes through the Midpoint X, Calculate the equation of the Perpendicular bisector of PQ

Solution:

P ( -4 , - 7)   , Q = ( 6 , 3)

a. the length of PQ

= √(6 - (-4))² + (3 - (-7))²

= √10² + 10²

= 10√2  unit

b. the gradient of PQ  

gradient  and slope are same thing.

= (3 - (-7))/(6 - (-4))

= 10/10

= 1

c. the co-ordinates of X

= (-4 + 6)/2 , ( - 7 + 3)/2

X =  (1 , - 2)

d. the intercept on the y axis

y -(-2)  = 1 (x - 1)

=> y  = x - 3

intercept on the y axis = - 3

e. the equation of the straight line which passes through the points P and Q.

y  = x - 3

f. State the gradient of the perpendicular bisector of PQ.

product of slope of perpendicular lines = - 1

Hence gradient of the perpendicular bisector of PQ.  = - 1

g. Given the fact that the perpendicular bisector passes through the  

X =  (1 , - 2)

y  - (-2)  = - 1(x - 1)

=> y + 2  = - x + 1

=> x + y = - 1

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