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Example Questions
Example Question #1 : Midpoint Formula
What is the coordinates of the point exactly half way between (-2, -3) and (5, 7)?
We need to use the midpoint formula to solve this question.
In our case
and
Therefore, substituting these values in we get the following:
Example Question #1 : Midpoint Formula
Find the midpoint between
and .
Write the midpoint formula.
Substitute the points.
The answer is:
Example Question #1 : Other Coordinate Geometry
On the coordinate plane, two lines intersect at the origin. One line passes through the point
; the other, .Give the measures of the acute angles they form at their intersection (nearest degree).
If
is the measure of the angles that two lines with slopes and form, then,
The slopes of the lines can be found by applying the slope formula
using the known points.
For the first line, set
:
The inverse tangent of this is
,
making this the angle this line forms with the
-axis.
For the second line, set
:
The inverse tangent of this is
making this the angle this line forms with the
-axis.Subtract:
Taking the inverse tangent:
.
Rounding to the nearest degree, this is
.Example Question #11 : Coordinate Geometry
In the figure below, regular hexagon
has a side length of . Find the y-coordinate of point .
From the given information, we know that the coordinate for
must be .Recall that the interior angle of a regular hexagon is
. Thus, we can draw in the following triangle.Since we know that this is a
triangle, we know that the sides must be as marked, in the ratio of . Thus, the y-coordinate of must be .Certified Tutor
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All SAT II Math II Resources
