Question

4.
what will be the new position of the given point (3, -5) after reflection across
the y - axis?
a) (3, 5) b) (-3, -5) c) (-3, 5) d) (3, -5)
what will be the new position of the given point (-6, 8) after rotating
90° clockwise about the origin?
a) (6, 8) b) (6, -8) c) (8, -6) d) (8, 6)
what will be the new position of the given point (7, 4) after translation of
2 units left and 4 units up?
a) (5, 8) b) (9, -8) c) (5, -8) d) (9, 8)

Explanation:

First Question: Reflection across the y - axis

Step1: Apply the reflection rule

When reflecting a point \((x,y)\) across the \(y\) - axis, the rule is \((x,y)\to(-x,y)\). For the point \((3,-5)\), \(x = 3\) and \(y=-5\). After applying the rule, the new \(x\) - coordinate is \(-3\) and the \(y\) - coordinate remains \(-5\).

Second Question: Rotation \(90^{\circ}\) clockwise about the origin

Step1: Apply the rotation rule

The rule for a \(90^{\circ}\) clockwise rotation about the origin is \((x,y)\to(y,-x)\). For the point \((-6,8)\), \(x=-6\) and \(y = 8\). After applying the rule, the new \(x\) - coordinate is \(8\) and the new \(y\) - coordinate is \(6\) (since \(-x=-(-6) = 6\)).

Third Question: Translation

Step1: Apply the translation rule

The rule for a translation of \(a\) units left and \(b\) units up is \((x,y)\to(x - a,y + b)\). Here \(a = 2\) and \(b=4\), and the point is \((7,4)\). So \(x=7-2=5\) and \(y=4 + 4=8\).

Answer:

1. B. \((-3,-5)\)
2. D. \((8,6)\)
3. A. \((5,8)\)