Question

10. A point P lies on the x-axis and another point
Q lies on the y-axis.
(i) Write the ordinate of point P.
(ii) Write the abscissa of point Q.
(iii) If the abscissa of point P is -12 and the
ordinate of point Q is -16; calculate the
length of line segment PQ.​

Answer 1

SOLUTION

GIVEN

A point P lies on the x-axis and another point Q lies on the y-axis.

TO DETERMINE

(i) The ordinate of point P.

(ii) The abscissa of point Q.

(iii) If the abscissa of point P is -12 and the ordinate of point Q is -16; calculate the length of line segment PQ.

CONCEPT TO BE IMPLEMENTED

1. For any point (x, y)

Abscissa = x

Ordinate = y

2. Any point on x axis is of the form (x, 0) & on y axis is of the form (0,y)

EVALUATION

Here it is given that A point P lies on the x-axis and another point Q lies on the y-axis.

(i) Since the point P lies on x axis

So the ordinate of P = 0

(ii) Since the point Q lies on y axis

So the abscissa of Q = 0

(iii) If the abscissa of point P is -12

Then the coordinates of P is ( - 12,0)

The ordinate of point Q is -16

∴ Ordinate of Q is ( 0,-16)

∴ The length of the line segment PQ is

$\sf{ = \sqrt{ {( - 12 - 0)}^{2} + {(0 + 16)}^{2} } } \: \: \: \: unit$

$\sf{ = \sqrt{144 + 256 } } \: \: \: \: unit$

$\sf{ = \sqrt{ 400 } } \: \: unit$

$\sf{ = 20 \: \: unit }$

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