The option B represents the correct match for the required pair of triangles.
Further explanation:
Step 1:
For option A the [tex]\triangle{QRA}[/tex] is mapped over the [tex]\triangle{LRK}[/tex], first reflecting across side [tex]QR[/tex] and then further reflecting across the side [tex]AR[/tex].
Thus, the [tex]\triangle QRA[/tex] and [tex]LRK[/tex] are not mapped together using a translation and a reflection.
Step 2:
For option B the [tex]\triangle QRA[/tex] is mapped over the [tex]\triangle LPK[/tex] , first reflecting across side [tex]QR[/tex] and then further translating in horizontal direction.
Thus, the [tex]\triangle QRA[/tex] and [tex]LPK[/tex] are mapped together using a translation and a reflection.
Step 3:
For option C the [tex]\triangle QRA[/tex] is mapped over the [tex]\triangle LPK[/tex] ,first translating in horizontal direction and then further translating in vertical direction.
Thus, the [tex]\triangle QRA[/tex] and [tex]LPK[/tex] are not mapped together using a translation and a reflection.
Step 4:
For option D the [tex]\triangle QRA[/tex] is mapped over the [tex]\triangle LRK[/tex] , first translating in horizontal direction and then further rotating about the point [tex]R[/tex].
Thus, the [tex]\triangle QRA[/tex] and [tex]LRK[/tex] are not mapped together using a translation and a reflection.
Therefore, the option B represents the correct match for the required pair of triangles.
Learn more:
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Answer Details:
Grade: Senior School
Subject: Mathematics
Chapter: Coordinate geometry.
Keywords:
triangle ABC, is shown on the graph, rotated 270° about the origin, rotation,degrees, transformation geometry, translation, reflection, dilation, multiplier, vertex matrix, initial coordinate, the image, rule, describestriangle, similar, similarity, ratio of sides, right triangle, similar triangle, ratio of sides, equal angles, square of hypotenuse, sum, square of legs, sum of square of legs, sum of angle of triangle, property of triangle, triangle ABC.
