Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

2 The diagram shows the points
A(0,-1),B(p,p) and
C(p,q).
(a) Given that the length of
AB is 5 units, find the value of
p.

$2$ The diagram shows the points $A(0,-1), B(p, p)$ and $C(p, q)$ . $\newline$ (a) Given that the length of $A B$ is $5$ units, find the value of $p$ .

View step-by-step help

View step-by-step help

Write a linear equation from two points

Full solution

Q.

2

The diagram shows the points

A(0,-1), B(p, p)

and

C(p, q)

.

\newline

(a) Given that the length of

A B

is

5

units, find the value of

p

.

Calculate distance formula: Calculate the distance between points $A(0,-1)$ and $B(p,p)$ using the distance formula: $d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}$ .
Substitute coordinates into formula: Substitute the coordinates of $A$ and $B$ into the distance formula: $d = \sqrt{((p - 0)^2 + (p - (-1))^2)}$ .
Simplify expression: Simplify the expression: $d = \sqrt{p^2 + (p + 1)^2}$ .
Set distance equal to $5$ : Since $AB$ is $5$ units, set the distance equal to $5$ : $5 = \sqrt{p^2 + (p + 1)^2}$ .
Square both sides: Square both sides to remove the square root: $25 = p^2 + (p + 1)^2$ .
Expand squared term: Expand the squared term: $25 = p^2 + p^2 + 2p + 1$ .
Combine like terms: Combine like terms: $25 = 2p^2 + 2p + 1$ .
Set equation to zero: Subtract $25$ from both sides to set the equation to zero: $0 = 2p^2 + 2p - 24$ .
Divide entire equation: Divide the entire equation by $2$ to simplify: $0 = p^2 + p - 12$ .
Factor quadratic equation: Factor the quadratic equation: p + \(4)(p - $3$ ) = $0$ \
Solve for $p$ : Set each factor equal to zero and solve for $p$ : $p + 4 = 0$ or $p - 3 = 0$ .
Final solution: Solve for $p$ : $p = -4$ or $p = 3$ .
Final solution: Solve for $p$ : $p = -4$ or $p = 3$ .Since $p$ is a coordinate, it cannot be negative in this context; therefore, $p = 3$ .

More problems from Write a linear equation from two points

Question

(0, 4)

satisfy the equation

y = x

?

\newline

Choices: [[yes]][[no]]

Posted 2 months ago

Question

Find the slope of the line

y = -4x + \frac{2}{5}

\newline

Write your answer as an integer or as a simplified proper or improper fraction.

Posted 1 month ago

Question

Rewrite the following equation in slope-intercept form.

\newline

y + 8 = -8(x - 10)

\newline

Write your answer using integers, proper fractions, and improper fractions in simplest form.

\newline

Posted 1 month ago

Question

y

-intercept of the line

14x - 16y = -10

\newline

Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

\newline

Posted 1 month ago

Question

q

\frac{-2}{3}

r

is perpendicular to

q

. What is the slope of line

r

\newline

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

\newline

\_\_\_\_\_

Posted 1 month ago

Question

Find the slope of the line

y + 3 = -\frac{1}{18}(x + 6)

\newline

Write your answer as an integer or as a simplified proper or improper fraction.

Posted 1 month ago

Question

p

has an equation of

y = -8x + 6

q

, which is perpendicular to line

p

, includes the point

(2, -2)

. What is the equation of line

q

?

\newline

Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

\newline

Posted 1 month ago

Question

Is the graph of this equation a horizontal or vertical line?

\newline

x = 7

\newline

\newline

\text{(A)horizontal line}

\newline

\text{(B)vertical line}

Posted 2 months ago

Question

Rewrite the following equation in standard form.

\newline

y = -10x + 7

\newline

Hint: The standard form of a linear equation is

\newline

Ax + By = C

A

B

are not both zero, and

A

B

C

are integers whose GCF is

1

Posted 2 months ago

Question

A line with a slope of

9

passes through the point

(9,9)

. What is its equation in point-slope form?

\newline

Use the specified point in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

\newline

y - \underline{\hspace{1cm}} = \underline{\hspace{1cm}} (x - \underline{\hspace{1cm}})

Posted 1 month ago