Calculate the gradient of the line segment QP, given the coordinates of Q as (0, −2) and P as (1, 1).

Step 1: Identify the coordinates of points Q and P. The coordinates are given as Q(0; −2) and P(1; 1). Step 2: Use the gradient formula. The formula for the gradient m between two points (x₁, y₁) and (x₂, y₂) is: m = (y₂ − y₁)/(x₂ − x₁); Let (x₁, y₁) = Q(0, −2) and (x₂, y₂) = P(1, 1). Step 3: Substitute the coordinates into the formula and calculate. mQP = (1 − (−2))/(1 − 0); mQP = (1 + 2)/(1); mQP = 3/1; mQP = 3 The gradient of QP is 3.

Calculate the gradient of the line segment QP, given the coordinates of Q as (0, −2) and P as (1, 1).

Step 1: Identify the coordinates of points Q and P. The coordinates are given as Q(0; −2) and P(1; 1). Step 2: Use the gradient formula. The formula for the gradient m between two points (x₁, y₁) and (x₂, y₂) is: m = (y₂ − y₁)/(x₂ − x₁); Let (x₁, y₁) = Q(0, −2) and (x₂, y₂) = P(1, 1). Step 3: Substitute the coordinates into the formula and calculate. mQP = (1 − (−2))/(1 − 0); mQP = (1 + 2)/(1); mQP = 3/1; mQP = 3 The gradient of QP is 3.

Solved: Calculate the gradient of the line segment QP…

Identify the coordinates of points Q and P.
The coordinates are given as $Q(0; -2)$ and $P(1; 1)$ .
Use the gradient formula.
The formula for the gradient $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Let $(x_1, y_1) = Q(0, -2)$ and $(x_2, y_2) = P(1, 1)$ .
Substitute the coordinates into the formula and calculate.
$m_{QP} = \frac{1 - (-2)}{1 - 0}$ $m_{QP} = \frac{1 + 2}{1}$ $m_{QP} = \frac{3}{1}$ $m_{QP} = 3$
The gradient of QP is $\text{3}$ .

Calculate the gradient of the line segment QP, given the coordinates of Q as (0, -2) and P as (1, 1).

Answer

Step-by-step solution

Identify the coordinates of points Q and P.

Use the gradient formula.

Substitute the coordinates into the formula and calculate.

Try one yourself

Still stuck on this one?

More Mathematics Questions