Question

29. Find the values of y for which the distance between the points A(2,-3) and B(10,y) is 10 units.
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Answer 1

ANSWER:-

Given:

The distance between the points A(2,-3) & B(10,y) is 10 units.

To find:

Find the value of y.

Solution:

We know that the formula of the distance is;

$= > d = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} }$

So,

⚫x1= 2 & x2= 10

⚫y1= -3 & y2= y

$= > d = \sqrt{( {10 - 2)}^{2} + ( {y - ( - 3)}^{2} } = 10 \\ \\ = > \sqrt{(8) {}^{2} + (y + 3) {}^{2} } = 10$

Squaring both sides, we get;

=) (8)² + (y+3)² = 100

=) 64 + (y+3)² = 100

=) (y+3)² = 100 - 64

=) (y+3)² = 36

=) (y+3)² = (6)²

=) y+3 = 6

=) y= 6 -3

=) y= 3

Hence,

The value of y is 3.

Hope it helps ☺️