Question

An artist designed a badge for a school club. Figure ABCD on the coordinate grid below shows the shape of the badge.

The badge is enlarged and plotted on the coordinate grid as figure JKLM with point J located at (2, -2) and point M located at (5, 4).

Which of these could be the coordinates for point L?

(2,4)

(8, 4)

(5, 1)

(5, 7)

Answer 1

(8, 4)

Explanation:

AD is enlarged to JM

AD² = 2² + 1² = 4 + 1 =5

AD = √5

then you plug in JM

JM² = 6² + 3² = 36 + 9 = 45

JM = √45 = 3 √5

so if

JM=3 AD

then

ML= 3 DC

then you add

5+3=8

the coordinates for point L are (8, 4)

Answer 2

Option B is right.

Explanation:

Given that an artist designed a badge for a school club.

ABCD is given in the picture.

AD =
`√((-7+8)^2 +(7-5)^2) \\=√(5)`

If JKLM is enlargement of ABCD, then scale factor would b the ratio of AD to JM

JM =
`√((5-2)^2+(4+2)^2) \\=√(45) \\3√(5)`

Scale factor = 3

AB = 3 hence JK = 9

DC = 1 and so ML = 3

ML is parallel to x axis with a distance of 3 units.

COordinates of L = (5+3, 4) = (8,4)

Option B is right