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प्रश्न
Find the image of the point A(5, –3) under reflection in the point P(–1, 3).
उत्तर
Image of the point A(5, –3) under reflection in the point P(–1, 3)
Let B(x, y) be the point of reflection of A(5, –3) under P(–1, 3)
∴ Point P is mid-point of AB
∴ `-1 = (5 + x)/2`
`=>` –2 = 5 + x
`=>` x = –2 – 5 = –7 and `3 = (-3 + y)/2`
`=>` 6 = –3 + y
`=>` y = 6 + 3 = 9
∴ Co-ordinates of B are (–7, 9) which is the image of point A.
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संबंधित प्रश्न
Calculate the co-ordinates of the point P which divides the line segment joining: A (–4, 6) and B (3, –5) in the ratio 3 : 2
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In what ratio does the point (1, a) divide the join of (–1, 4) and (4, –1)? Also, find the value of a.
Calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by point p(x,3). Also, find x
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M is the mid-point of the line segment joining the points A(0, 4) and B(6, 0). M also divides the line segment OP in the ratio 1 : 3. Find :
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- length of BP
Find the image of the point A(5,3) under reflection in the point P(-1,3).
Find the image of the point A(5,3) under reflection in the point P(-1,3).
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= `a(1/t^2 + 1) = (a(t^2 + 1))/t^2`
Now `(1)/"SP" + (1)/"SQ" = (1)/(a(t^2 + 1)) + (1 xx t^2)/(a(t^2 + 1)`
= `((1 + t^2))/(a(t^2 + 1)`
`(1)/"SP" + (1)/"SQ" = (1)/a`.
From the adjacent figure:
(i) Write the coordinates of the points A, B, and
(ii) Write the slope of the line AB.
(iii) Line through C, drawn parallel to AB, intersects Y-axis at D. Calculate the co-ordinates of D.
