Triangle OA₁B₁ is the reflection of triangle OAB in origin, where A₁ (4, -5) is the image of A and B₁ (-7, 0) is the image of B.
``` kboatpngend
(i) Write down the co-ordinates of A and B and draw a diagram to represent this information.
(ii) Give a special name to the quadrilateral ABA₁B₁. Give reason.
(iii) Find the co-ordinates of A₂, the image of A under reflection in x-axis followed by reflection in y-axis.
(iv) Find the co-ordinates of B₂, the image of B under reflection in y-axis followed by reflection in origin.

Question

Triangle OA₁B₁ is the reflection of triangle OAB in origin, where A₁ (4, -5) is the image of A and B₁ (-7, 0) is the image of B.
``` kboatpngend
(i) Write down the co-ordinates of A and B and draw a diagram to represent this information.
(ii) Give a special name to the quadrilateral ABA₁B₁. Give reason.
(iii) Find the co-ordinates of A₂, the image of A under reflection in x-axis followed by reflection in y-axis.
(iv) Find the co-ordinates of B₂, the image of B under reflection in y-axis followed by reflection in origin.

KnowledgeBoat · Accepted Answer

(i) From graph, Coordinates of A = (-4, 5) and B = (7, 0). (ii) By distance formula, OA = units. OA₁ = units. OB = OB₁ = 7 units. Since, diagonals bisect each other. Hence, ABA₁B₁ is a parallelogram. (iii) We know that, On reflection in x-axis, the sign of y-coordinate changes. ∴ (-4, 5) on reflection in x-axis gives (-4, -5). We know that, On reflection in y-axis, the sign of x-coordinate changes. ∴ (-4, -5) on reflection in y-axis gives (4, -5). ∴ A₂ = (4, -5). Hence, coordinates of A₂ = (4, -5). (iv) We know that, On reflection in y-axis, the sign of x-coordinate changes. ∴ (7, 0) on reflection in y-axis gives (-7, 0). We know that, On reflection in x-axis, the sign of y-coordinate changes. ∴ (-7, 0) on reflection in x-axis gives (-7, 0). ∴ B₂ = (-7, 0). Hence, coordinates of B₂ = (-7, 0).

Mathematics

Reflection

Related Questions

Find the values of m and n, in each case; if :
(i) (4, -3) on reflection in x-axis gives (-m, n).
(ii) (m, 5) on reflection in y-axis gives (-5, n - 2)
(iii) (-6, n + 2) on reflection in origin gives (m + 3, -4).

In what ratio does the point M(p, -1) divide the line segment joining the points A(1, -3) and B(6, 2) ? Hence, find the value of p.

A(-4, 4), B(x, -1) and C(6, y) are the vertices of △ABC. If the centroid of this triangle ABC is at the origin, find the values of x and y.