Oxford University MAT 2020 Solved Papers

Question : 1 of 10

Marks: +1, -0

A square has centre

(3,4)

and one corner at

(1,5)

. Another corner is at

$(1,3)$ ,
$(5,5)$ ,
$(4,2)$ ,
$(2,2)$ ,
$(5,2)$ .

Solution:

The centre is at

(3,4)

and one corner is at

(1,5)

, which is a displacement of

(-2,1)

. There's another corner opposite, at

(3,4)-(-2,1)=(5,3)

, but this is not one of the options. To find the other corners, we need to find a vector with equal magnitude, but at right-angles to

(-2,1)

. Rotating by

90^{∘}

gives

(1,2)

. The other corners are at

(3,4) ±(1,2)

, which includes

(2,2)

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