Question

if the length of a line segment is √10 units if one end is at (2,-3)and the abscissa of the second end is 5 show that it ordinate either -2 or -4 pls answer this question proper ans​

Answer 1

SOLUTION

GIVEN

The length of a line segment is √10 units if one end is at (2,-3) and the abscissa of the second end is 5

TO PROVE

The ordinate either - 2 or - 4

CONCEPT TO BE IMPLEMENTED

For the given two points $\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$ the distance between the points

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

EVALUATION

Here it is given that the length of a line segment is √10 units if one end is at (2,-3) and the abscissa of the second end is 5

Let ordinate = y

So by the given condition

$\sf{ \sqrt{ {(5 - 2)}^{2} + {(y + 3)}^{2} } = {( \sqrt{10} )} }$

$\sf{ \implies \: \sqrt{ {(3)}^{2} + {(y + 3)}^{2} } = \sqrt{10} }$

$\sf{ \implies \:9 + {(y + 3)}^{2} = 10 }$

$\sf{ \implies \: {(y + 3)}^{2} = 1 }$

$\sf{ \implies \: {(y + 3)}= \pm \: 1 }$

Now y + 3 = 1 gives y = - 2

Again y + 3 = - 1 gives y = - 4

Hence ordinate is either - 2 or - 4

Hence proved

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Answer 2

Answer:

The length of a line segment is 10. If one end point is 2,3and the abscissa of the

second end point is 10, show that its ordinate is e