Lines - ISEE Lower Level Quantitative Reasoning

The distance formula is .

Let and .

Plug these two points into the distance formula:

Let , and let be the end point we are looking for.

Recall the distance formula:

Squaring the distance formula gives .

Plug this squared distance formula and solve for :

Substitute each response into this equation to see which one is false. The only response that doesn't work is .

The distance formula is .

Let and .

Plug these points into the distance formula:

The distance formula is given by .

Square both sides:

Now, let , and let be the end point we are looking for.

Plug into the squared distance formula and solve for :

Alternatively, you can plug in the answer choices and see which point makes the above equation untrue. The point matches this description and is therefore the correct answer.

The distance formula is given by .

Let and :

The distance formula is given by .

Let and :

The distance formula is .

Let and :

To find the length of a line on the number line when one point is negative and the other is positive, you must the the distances of both from zero. is spaces from zero where is the other point is just . So the distance is .

The distance formula is .

Let and :

A line of symmetry is a line that divides a polygon in half and each half is a mirror image of the other. In other words, you can fold the polygon over the symmetry line and each half matches up perfectly.

For a square there are four lines of symmetry. Two are from the diagonals of the square and two are from connecting the midpoints of the opposite sides.

A key characteristic of a rectangle, parallelogram, and trapezoid is the fact that they each have at least one pair of lines that run parallel to each other. The only option that has lines that may not run parallel to each other is the quadrilateral, which must simply have four sides but has no specifications about parallelism.

While drawing a line across a rectangle (so that it bisects 2 sides) can result in 2 quadrilaterals, squares, or rectangles, a line drawn from one corner to the furthest corner results in two triangles. Therefore, the correct answer choice is 2 triangles.

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry.

If no, then the line does not represent a line of symmetry.

This line does not represents a line of symmetry because if you fold on the black line, one side will not lay on top of the other with parts that match up.

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry.

If no, then the line does not represent a line of symmetry.

This line represents a line of symmetry because if you fold on the black line, then one side would lay on top of the other and the parts would match up.

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry.

If no, then the line does not represent a line of symmetry.

This line does not represents a line of symmetry because if you fold on the black line, one side will not lay on top of the other with parts that match up.

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry.

If no, then the line does not represent a line of symmetry.

This line represents a line of symmetry because if you fold on the black line, then one side would lay on top of the other and the parts would match up.

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry.

If no, then the line does not represent a line of symmetry.

This line does not represents a line of symmetry because if you fold on the black line, one side will not lay on top of the other with parts that match up.

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry.

If no, then the line does not represent a line of symmetry.

This line represents a line of symmetry because if you fold on the black line, then one side would lay on top of the other and the parts would match up.

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry.

If no, then the line does not represent a line of symmetry.

This line does not represents a line of symmetry because if you fold on the black line, one side will not lay on top of the other with parts that match up.

When you are trying to decide if a line represents a line of symmetry you can think about folding the figure across that line. Once you make the fold, do all of the parts line up on top?

If yes, then the line represents a line of symmetry.

If no, then the line does not represent a line of symmetry.

This line does not represents a line of symmetry because if you fold on the black line, one side will not lay on top of the other with parts that match up.