This question should be answerd using taxicab geometry A bui

This question should be answerd using taxicab geometry.

A builder wants to put up an apartment building within six blocks of the shopping center (-3, 0) and within four blocks of the tennis courts (2,2). Where can he build? From the list below, select all points that are within the builder\'s range.

NOTE: This question is graded as \"Right minus wrong\".

B(1, 1)

D(-1, 2)

A(2, 2)

I(1, -2)

G(-3, 0)

F(-3, 2)

E(2, 0)

C(1, 3)

H(-1, -1)

J(1, -1)

Solution

Assumption

Each block measures one unit.

Let the shopping center be at S(-3,0) and the tennis court be at C(2,2)

thus as per taxicab geometry, the distance between the two points S and C will be given by

SC=|(-3)-2|+|0-2|

thus, SC=7

Now let us check distance of each point from S and C and check which are the point which lie within 6 units to S and 4 units to C respectively.

For point B

d(BS) =5 and d(BC)=2

Clearly d(BS)<6 and d(BC)<4 (as per the question)

Hence point B lies within range of builder.

Similarly for D(-1,2)

d(DS)=4 and d(DC)=3 . Satisfies

for A(2,2)

d(AS)=7 (>6) Hence doesnt satisfy

for I(1,-2)

d(IS)=6 and d(IC)=5 (doesnt satisfy since d(IC)>4)

for G(-3,0)

d(GS)=0 and d(GC)=7 (doesnt satisfy since d(GC)>4)

for F(-3,2)

d(FS)=2 and d(FC)=5 (doesnt satisfy since d(FC)>4)

For E(2,0)

d(ES)=5 and d(EC)=2 .Satisfies

For C(1,3)

d(CS)=7 (doesnt satisfy since d(CS)>6)

for H(-1,-1)

d(HS)=3 and d(HC)=6 (doesnt satisfy since d(HC)>4)

for J(1,-1)

d(JS)=5 and d(JC)=4. Satisfies.