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 Text Solution 5`5sqrt(2)``2sqrt(5)`10 Answer : B Solution : `:.` Distance between the points `(x_(1),y_(1))and (x_(2),y_(2)),` <br> d`=sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2))` <br> Here, `x_(1)=0,y_(1)=5andx_(2)=0` <br> `:.` Distance between the points (0,5) and (-5,0) <br> `=sqrt((-5-0)^(2)+(0-5)^(2))` <br> `=sqrt(25+25)=sqrt(50)=5sqrt(2)` No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Answer Hint: To solve this question, we should know about a few concepts of coordinate geometry like distance formula, that is distance between two points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ can be calculated using the formula, $\sqrt{{{\left( {{x}_{1}}-{{x}_{2}} \right)}^{2}}+{{\left( {{y}_{1}}-{{y}_{2}} \right)}^{2}}}$. Also, we need to take care of the signs while solving this question. Complete step-by-step solution - In this question, we have been given two points, that is, (0, 5) and (-5, 0). And we have been asked to find the distance between them. For that we require the knowledge about distance formula of coordinate geometry, which states that distance between any two given coordinates like $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is given by $\sqrt{{{\left( {{x}_{1}}-{{x}_{2}} \right)}^{2}}+{{\left( {{y}_{1}}-{{y}_{2}} \right)}^{2}}}$. Now, we will consider ${{x}_{1}}=0,{{y}_{1}}=5$ and ${{x}_{2}}=-5,{{y}_{2}}=0$. We will put these values in the distance formula, we get the distance between the two points (0, 5) and (-5, 0) as,$\sqrt{{{\left[ 0-\left( -5 \right) \right]}^{2}}+{{\left[ 5-0 \right]}^{2}}}$ Simplifying it further, we get,$\begin{align} & \sqrt{{{\left[ 0+5 \right]}^{2}}+{{\left[ 5-0 \right]}^{2}}} \\ & \Rightarrow \sqrt{{{\left( 5 \right)}^{2}}+{{\left( 5 \right)}^{2}}} \\ \end{align}$Now, we know that ${{5}^{2}}=5\times 5=25$. So, we will get the distance between (0, 5) and (-5, 0) as, $=\sqrt{25+25}$ Now, we know that 25 +25 = 50, so we will get $\sqrt{50}$. We know that 50 can be expressed as $25\times 2$, where 25 can be represented as ${{5}^{2}}$. So, we will get, $\sqrt{{{5}^{2}}\times 2}$, which can be further written as, $\sqrt{{{5}^{2}}}\times \sqrt{2}$. We know that the square root of square of any term gives us the same term, so we get, $5\sqrt{2}$. Hence, we can say that the distance between the points (0, 5) and (-5, 0) is $5\sqrt{2}$. Therefore, the correct answer is option B.Note: We can also solve this question by plotting points on graph and then applying the Pythagoras theorem. Like the figure below,
Solution: We know that the formula to find the distance between two points P(x₁, y₁) and Q(x₂, y₂) is Distance = \(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\) It is given that We have to find the distance between the points (0, 5) and (–5, 0) Substituting these values in the equation we get \(Distance=\sqrt{(-5-0)^{2}+(0 - 5)^{2}}\) So we get Distance between the points = √(25 + 25) = √50 = 5√2 Distance between the points = 5√2 units Therefore, the distance between the points (0, 5) and (–5, 0) is 5√2 units. ✦ Try This: The distance between the points (0, 4) and (-4, 0) is We know that the formula to find the distance between two points P(x₁, y₁) and Q(x₂, y₂) is Distance = \(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\) It is given that We have to find the distance between the points (0,4) and (-4, 0) Substituting these values in the equation we get Distance = \(\sqrt{(-4-0)^{2}+(0 - 4)^{2}}\) So we get Distance between the points = √(16 + 16) = √32 = 4√2 Distance between the points = 4√2 units Therefore, the distance between the points (0, 4) and (-4, 0) is 4√2 units. ☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7 NCERT Exemplar Class 10 Maths Exercise 7.1 Problem 4 Summary: The distance between the points (0, 5) and (–5, 0) is 5√2 units ☛ Related Questions:
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What is the distance between the points 0 5 and - 50
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