Question

A line segment is of length 10 units.If the coordinates of its one end are (1,4) and the ordinate of the other end is -2 then its abscissa is

Answer 1

Given :-

• Length of Line segment = 10 units.
• Coordinate at one end = (1,4) .
• Coordinate at other end = (x, -2) .

To Find :-

• Value of x = Abscissa ?

Solution :-

Distance between two points (x1,y1) and(x2,y2) is given by √[(x2-x1)² + (y2-y1)²]

Here we Have :-

→ x1 = 1

→ x2 = x

→ y1 = 4

→ y2 = -2

→ D = 10 units .

Putting values we get :-

→ √[(x-1)² + (-2-4)² ] = 10

Squaring both sides,

→ (x-1)² + 36 = 100

→ x² - 2x + 1 + 36 = 100

→ x² - 2x + 37 - 100 = 0

→ x² -2x - 63 = 0

Splitting The Middle Term now,

→ x² - 9x + 7x - 63 = 0

→ x(x - 9) +7(x - 9) = 0

→ (x - 9)(x + 7) = 0

Putting Both Equal to Zero,

→ x - 9 = 0

→ x = 9

Or,

→ x + 7 = 0

→x = (-7)

Hence, its abscissa is (-7) or 9.

Answer 2

ANSWER:

Let , A = ( 1 , 4) & B = ( a , - 2)

Given,

Distance between two points = 10 units.

As we know,

$distance \: between \: two \: points \: = \sqrt{( { x_{2} - x_{1} ) }^{2} + {(y _{2} - y_{1} }^{2} }$

Substitute the values here.

$10 = \sqrt{( {a - 1)}^{2} + ( - 2 - 4) ^{2} } \\ \\ 10 = \sqrt{ {(a - 1)}^{2} + {( - 6)}^{2} } \\ \\ 10 = \sqrt{ {(a - 1)}^{2} + 36 }$

By squaring on both sides ,

$100 = {(a - 1)}^{2} + 36 \\ \\ 100 - 36 = {(a - 1)}^{2} \\ \\ 64 = {(a - 1)}^{2} \\ \\ a - 1 = \sqrt{64} \\ \\ a - 1 = (8) \: or \: ( - 8) \\ \\ a = 8 + 1 \: (or) \: - 8 + 1 \\ \\ a = 9 \: (or) \: - 7.$