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Example Questions
Example Question #1 : How To Find The Length Of A Line With Distance Formula
Let W and Z be the points of intersection between the parabola whose graph is y = –x² – 2x + 3, and the line whose equation is y = x – 7. What is the length of the line segment WZ?
7
7√2
4√2
4
7√2
First, set the two equations equal to one another.
–x² – 2x + 3 = x – 7
Rearranging gives
x² + 3x – 10 = 0
Factoring gives
(x + 5)(x – 2) = 0
The points of intersection are therefore W(–5, –12) and Z(2, –5)
Using the distance formula gives 7√2
Example Question #1 : Distance Formula
In an xy-plane, what is the length of a line connecting points at (–2,–3) and (5,6)?
9.3
11.4
12.5
7.5
11.4
Use the distance formula:
D = √((y2 – y1)2 + (x2 – x1)2)
D = √((6 + 3)2 + (5 + 2)2)
D = √((9)2 + (7)2)
D = √(81 + 49)
D = √130
D = 11.4
Example Question #3 : How To Find The Length Of A Line With Distance Formula
What is the distance between points and
, to the nearest tenth?
The distance between points and
is 6.4. Point
is at
. Point
is at
. Putting these points into the distance formula, we have
.
Example Question #111 : Algebra
What is the slope of the line between points and
?
The slope of the line between points and
is
. Point
is at
. Point
is at
. Putting these points into the slope formula, we have
.
Example Question #5 : How To Find The Length Of A Line With Distance Formula
What is the distance between and
?
Let and
and use the distance formula:
. The distance formula is a specific application of the more general Pythagorean Theorem:
.
Example Question #1 : How To Find The Length Of A Line With Distance Formula
What is the distance, in coordinate units, between the points and
in the standard
coordinate plane?
The distance formula is , where
= distance.
Plugging in our values, we get
Example Question #1 : How To Find The Length Of A Line With Distance Formula
What is the distance between points and
?
Solution A:
Use the distance formula to calculate the distance between the two points:
Solution B:
Draw the two points on a coordinate graph and create a right triangle with sides 4 and 5. Using the Pythagorean Theorem, solve for the hypotenuse or the distance between the two points:
Example Question #1 : Distance Formula
What is the distance between (1,5) and (6,17)?
Let and
So we use the distance formula
and evaluate it using the given points:
Example Question #1 : Distance Formula
What is the area of a square with a diagonal that has endpoints at (4, –1) and (2, –5)?
5
100
10
20
25
10
First, we need to find the length of the diagonal. In order to do that, we will use the distance formula:
Now that we have the length of the diagonal, we can find the length of the side of a square. The diagonal of a square makes a 45/45/90 right triangle with the sides of the square, which we shall call s. Remember that all sides of a square are equal in length.
Because this is a 45/45/90, the length of the hypotenuse is equal to the length of the side multiplied by the square root of 2
The area of the square is equal to s2, which is 10.
Example Question #10 : How To Find The Length Of A Line With Distance Formula
Line segment has end points of
and
.
Line segemet has end points of
and
.
What is the distance between the midpoints?
The midpopint is found by taking the average of each coordinate:
and
The distance formula is given by
.
Making the appropriate substitutions we get a distance of 13.
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