Points in a Plane

Geometry Level pending

Points $A$ , $B$ , and $C$ lie in the same plane.

If $l(AB) = 9$ and $l(BC) = 4$ , which of the following statements can be true?

$1$ . $l(AC) = 13$

$2$ . $l(AC) = 5$

$3$ . $l(AC) = 8$

2

only

1

2

, and

3

1

only

2

and

3

only

1

and

2

only

1 solution

Anuj Shikarkhane
Sep 24, 2017

If A, B, C lie in a straight line, length AC can hold the values of $9+4=13$ and $9-4=5$ .

Don't hurry and select option 1 and 2. The points lie in the same plane, so they can also form the sides of a triangle. Hence, by triangle inequality, AC can also hold the value of $8$ .

Points in a Plane

1 solution

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