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प्रश्न
Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
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उत्तर १
We have to find a point on x-axis. Therefore, its y-coordinate will be 0.
Let the point on x-axis be (x, 0)
Distance between (x, 0) and (2, -5) = `sqrt((x-2)^2+(0-(-5))^2)`
= `sqrt((x-2)^2+(5)^2)`
Distance between (x, 0) and (-2, -9) = `sqrt((x-(-2))^2+(0-(-9))^2)`
= `sqrt((x+2)^2+(9)^2)`
By the given condition, these distances are equal in measure.
`sqrt((x-2)^2 +(5)^2)`
= `sqrt((x+2)^2+(9)^2)`
= (x - 2)2 + 25 = (x + 2)2 + 81
= x2 + 4 - 4x + 25
= x2 + 4 + 4x + 81
8x = 25 - 81
8x = -56
x = -7
Therefore, the point is (−7, 0).
उत्तर २
Let (x, 0) be the point on the x axis. Then as per the question, we have
⇒ `sqrt((x-2)^2 +(0+5)^2)`
⇒ `sqrt((x+2)^2 + (0-9)^2)`
⇒ `sqrt((x-2)^2 +(5)^2)=sqrt((x+2)^2 + (9)^2)`
⇒ (x - 2)2 + (5)2 = (x + 2)2 + (-9)2 ...(Squaring both sides)
⇒ x2 - 4x + 4 + 25 = x2 + 4x + 4 + 81
8x = 25 - 81
8x = -56
x = -7
Therefore, the point is (−7, 0).
संबंधित प्रश्न
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The distance between the point P(1, 4) and Q(4, 0) is ______.
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Read the following passage:
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Use of mobile screen for long hours makes your eye sight weak and give you headaches. Children who are addicted to play "PUBG" can get easily stressed out. To raise social awareness about ill effects of playing PUBG, a school decided to start 'BAN PUBG' campaign, in which students are asked to prepare campaign board in the shape of a rectangle: One such campaign board made by class X student of the school is shown in the figure.
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Based on the above information, answer the following questions:
- Find the coordinates of the point of intersection of diagonals AC and BD.
- Find the length of the diagonal AC.
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- Find the area of the campaign Board ABCD.
OR - Find the ratio of the length of side AB to the length of the diagonal AC.
- Find the area of the campaign Board ABCD.
