**10th grade math solution exercise 5.4 part 3:**

Here we are going to see solutions of some problems that we find in the exercise number 5.4

**Question 7 :**

Find the equation of the straight line which passes through the midpoint of the line segment joining (4, 2) and (3, 1) whose angle of inclination is 30° .

**Solution : **

Let us draw a rough diagram based on the given information.

From the above diagram, we come to know that we have to find the line passing through the point C.

Midpoint of AB = (x₁ + x₂)/2, (y₁ + y₂)/2

A(4, 1) B(3, 2)

= (4 + 3)/2 , (1 + 2)/2

= C (7/2, 3/2)

From the angle of inclination of the required line, we have to find the slope.

m = tan θ ==> tan 30° ==> 1/√3

Equation of the required line :

(y - y₁) = m (x - x₁)

(y - (3/2)) = (1/√3) (x - (7/2))

√3 (y - (3/2)) = 1 (x - (7/2))

√3 (2y - 3) = 1 (2x - 7)

2√3 y - 3√3 = 2x - 7

2x - 2√3y - 7 + 3√3 = 0

Hence equation of the required line is 2x - 2√3y + (3√3 - 7) = 0

**Question 8 :**

Find the equation of the straight line passing through the points

(i) (-2, 5) and (3, 6)

**Solution : **

Equation of the line passing through two given points.

(y - y₁) /(y₂-y₁) = (x - x₁) /(x₂-x₁)

(x₁, y₁) ==> (-2, 5) and (x₂, y₂) ==> (3, 6)

(y-5)/(6 - 5) = (x - (-2))/(3 - (-2))

(y-5)/1 = (x+2)/(3 +2)

(y-5)/1 = (x +2)/5

5(y - 5) = 1(x + 2)

5y - 25 = x + 2

x - 5y + 2 + 25 = 0

x - 5y + 27 = 0

(ii) (0, -6) and (-8, 2)

Equation of the line passing through two given points.

(y - y₁) /(y₂-y₁) = (x - x₁) /(x₂-x₁)

(x₁, y₁) ==> (0, -6) and (x₂, y₂) ==> (-8, 2)

(y-(-6))/(2 - (-6)) = (x - 0)/(-8 - 0)

(y+6)/(2 + 6) = x/(-8)

(y+6)/8 = x/(-8)

(y + 6) = -x

x + y + 6 = 0

After having gone through the stuff given above, we hope that the students would have understood "10th grade math solution exercise 5.4 part3".

Apart from the stuff given above, if you want to know more about "10th grade math solution exercise 5.4 part3", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**