Question

What are the new vertices of quadrilateral KLMN if the quadrilateral is translated two units to the right and four units upward?

A. K′ = (–2,0), L′ = (1,0), M′ = (1,–3), N′ = (–2,–3)
B. K′ = (–0,0), L′ = (3,0), M′ = (3,–1), N′ = (0,–1)
C. K′ = (–2,–2), L′ = (1,–2), M′ = (1,–5), N′ = (–2,–5)
D. K′ = (–2,2), L′ = (1,2), M′ = (1,–1), N′ = (–2,–1)

Answer 1

Concept:

If we translate a point (x,y), towards 'a' units right to it then the coordinates become (x+a,y).

Similarly, if we translate a point (x,y) upwards 'b' units then the coordinates become (x,y+b).

Given:

Given the figure shows that the initial coordinates of points are,

K = (-4,-2); L = (-1,-2); M = (-1,-5); N = (-4,-5)

And quadrilateral KLMN is translated to two units to the right and four units upwards.

Find:

The new coordinates of the points K, L, M, N.

Solution:

Given that quadrilateral translated to two units right and four units upward, so each point will translate same way.

Initial coordinates of K  = (-4,-2)

New coordinates will be, K' = (-4+2, -2+4) = (-2,2)

Initial coordinates of L = (-1,-2)

New coordinates will be, L' = (-1+2,-2+4) = (1,2)

Initial coordinates of M = (-1,-5)

New coordinates will be, M' = (-1+2,-5+4) = (1,-1)

Initial coordinates of N = (-4,-5)

New coordinates will be, N' = (-4+2,-5+4) = (-2,-1)

Hence the correct option is (D) K′ = (–2,2), L′ = (1,2), M′ = (1,–1), N′ = (–2,–1).

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Answer 2

Answer:

K′ = (–2,2), L′ = (1,2), M′ = (1,–1), N′ = (–2,–1).

Step-by-step explanation:

Given:

Four-sided KLMN The quadrilateral will move two units to the right and four units upward if this is done.

To find:

New vertices

Solution:

A point's coordinates become (x+a,y) if we translate them in the direction of 'a' units right to it.

Similar to this, if we move a point (x,y) up 'b' units, the coordinates change to (x,y+b).

K's initial coordinates are: (-4,-2)

New coordinates will be, K' = (-4+2, -2+4) = (-2,2)

L's initial coordinates are: (-1,-2)

New coordinates will be, L' = (-1+2,-2+4) = (1,2)

M's initial coordinates are: (-1,-5)

New coordinates will be, M' = (-1+2,-5+4) = (1,-1)

N's initial coordinates are: (-4,-5)

New coordinates will be, N' = (-4+2,-5+4) = (-2,-1)

Name the type of quadrilateral formed by the vertices (-2, 0),

(3, 2), (2, -1) and (-3,-3). Give reasons.​

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