Question

Calculate the distance between the points (7, 4) and (-5, -3).​

Answer 1

Answer:

D = √193 units

or

D = 13.892 units

Step-by-step explanation:

Given:

(7, 4) and (-5, -3)

Calculate the distance

Solution:

$\rm \: Distance (D) = \sqrt{( x_{2} - x_{1}) {}^{2} + (y_{2} - y_{1) {}^{2} }}$

Now, substitute the values given:

$\rm \: D = \sqrt{ \{( - 5) - 7 \}^{2} + \{( - 3) - 4 {}^{} \} {}^{2} }$

$\rm \: D = \sqrt{ \{12 \}^{2} + \{( - 3) - 4 {}^{} \} {}^{2} }$

$\rm \: D = \sqrt{ 144 + \{( - 3) - 4 {}^{} \} {}^{2} }$

$\rm D = \sqrt{144 + \{ 7\}{}^{2} }$

$\rm \: D = \sqrt{144 + 49}$

$\boxed{\rm \: D = \sqrt{193}}$

$\boxed{\rm \: D =13 .892}$

Thus, Distance between the two given points will be √193 or √13.892 units.

Answer 2

Answer:

$\bf \sqrt{193}$ units or 13.9 units is the distance.

Explanation:

$\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 +(y_2 - y_1)^2}$

Given points: (7, 4) and (-5, -3)

Identify following:

$\sf x_2= 7$, $\sf x_1 = -5$, $\sf y_2 =4$, $\sf y_1 =-3$

Find distance:

$\rightarrow \sf \sqrt{(7 - (-5))^2 + (4 - (-3))^2} \quad = \quad \sqrt{144+49} \quad = \quad \sqrt{193} \quad \approx \ 13.9$