Question

Find the distance between P(x, y) and Q(x, y) when :( PQ is parallel to the
v-atis. (ii) PQ is parallel to the x-axis.
​

Answer 1

Distance between two points =

$\sqrt{ {(x_2-x_1)}^{2} + { (y_2-y_1)}^{2} }$

(i) when PQ is parallel to y-axis, which means that the value of x will remain same hence,

$PQ = \sqrt{ {(x_2-x_1)}^{2} + { (y_2-y_1)}^{2} } \\ where \: x_2 = x_1 \\ PQ = \sqrt{ {(x_2-x_2)}^{2} + { (y_2-y_1)}^{2} } \\ PQ = \sqrt{ { (y_2-y_1)}^{2} } \\ PQ = (y_2-y_1)$

(ii) when PQ is parallel to x-axis, which means that the value of y will remain same

$PQ = \sqrt{ {(x_2-x_1)}^{2} + { (y_2-y_1)}^{2} } \\ where \: y_2 = y_1 \\ PQ = \sqrt{ {(x_2-x_1)}^{2} + { (y_2-y_2)}^{2} } \\ PQ = \sqrt{ {(x_2-x_1)}^{2} } \\ PQ = (x_2-x_1)$

Answer 2

Answer:

i) modulus of y2 - y1

ii) modulus of x2 - x1

Step-by-step explanation:

i)

PQ is parallel to y-axis--> the x coordinate of both points is same. Hence the distance formula:

root over (y2-y1) whole squared, that is

| y2 - y1 | -- ( | | is modulus)

ii)

PQ is parallel to x- axis, then their y coordinate will be same. Hence the distance formula:

root over (x2-x1) whole squared, that is

| x2 - x1 | -- ( | | is modulus)

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