Question

Based on the shortest leg of the triangle illustrated, if a similar triangle on the coordinate plane has its shortest leg defined by the points (2, 3) and (8, 3), what is the third point? A) (2, -5) B) (2, -6) C) (2, -7) D) (2, -8)

Answer 1

None of the Answers are correct.

Explanation:

A similar triangle will have the same ratio of sides as the triangle illustrated.

The triangle illustrated has a ratio of 2: 4 or 1:2 of the short side to the long side. The similar triangle must have the same ratio.

The short side of the triangle (2,3) ( 8,3) has a length of 6.

`8- 2 = 6` for the x value so the short side has a length of 6

The long side of the triangle has a length of 12 in the y direction.

1:2 gives: 6:12 `2 xx 6 = 12`

The y value of the points given is 3, so the new value of y must be 3 plus or minus 12

3+12 = 15 3 -12 = -9

None of these points meet the criteria of a y value of 15 or -9

Answer 2

The point `(2,-6)` is one of the options given.

Explanation:

To work through this question, it will help to have a grid on hand to sketch the information given.

From the given triangle, we can see that the lengths of the arms of the right-angle are `2` units and `3` units. (the shortest side is `2` units long and vertical)

The second triangle is described as being similar, which means its sides are in the same ratio as the first, but the orientation can be different.

From the two given points (draw a quick sketch) the shortest side is seen to be horizontal and `6` units long. (`8-2 = 6`)

This means that the sides of the second triangle are all `3` times as long as the first.

The second side will therefore be `3xx3 = 9` units long.

There are 4 possible positions for the third point. `9` units up or down from `(2,3) or (8,3)` to form a right-angle.

The options are therefore: `(2,12) ; color(red)(((2,-6))) ; (8,12) ; (8,-6)`

Only the point `(2,-6)` is one of the options given.