# Find the value of p if the line joining (p, 4) and (6, -2) is…

**Find the value of p if the line joining (p, 4) and (6, -2) is perpendicular to the line joining (2, 9) and (-1, 3)**

**A.**** ****4**

**B.**** 3**

**C.**** **

**D.**** ****–****6**

**QUICK ANSWER…**

**D**

**DETAILS…**

**If two lines are perpendicular to each other, then it follows that the multiplication of their gradients will be equal to minus one.**

**That is,**

**if the gradient of one of the lines is = m****₁****,**

**and the gradient of the second line is = m****₂**

**then, m₁ × m₂ = – 1**

**from the question, the gradient of the first line m₁ = (change in y)/(change in x)**

**m₁ = (y₂ – y₁)/(x₂ – x₁)**

**where**

**x₁ = p**

**y₁ = 4**

**x₂ = 6**

**y₂ = -2**

**m₁ = (-2 – 4)/(6 – p)**

**m₁ = -6/(6 – p)**

**also for the second line, m₂ = (y₂ – y₁)/(x₂ – x₁)**

**where**

**x₁ = 2**

**y₁ = 9**

**x₂ = -1**

**y₂ = 3**

**m₂ = (3 – 9)/(-1 – 2)**

**m₂ = -6/-3 = 2**

**applying the rule: m₁m₂ = -1**

**-6/(6 – p) × 2 = -1**

**Doing the math to determine p, we have:**

**-12/(6 – p) = -1**

**-12 = -1(6 – p)**

**12 = 6 – p**

**Rearranging to take p the other side and 12 the other way,**

**p = 6 – 12**

**p = -6**

**Now for the right answer to the above question:**

**Option A is incorrect.****Option B is incorrect.****C is not correct.****D is the correct answer.**

**KEY-POINTS…**

**You may please note these/this:**

**If two lines are perpendicular, then the product of their gradients must be = -1****m₁m₂ = -1, where m****₁****= gradient of line 1, m****₂****= gradient of line 2.****If you love our answers, you can login to comment and say hi to us at the comment section…**

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**/ culled from 2020 JAMB-UTME mathematics past question 22 /**