**10th grade math solution exercise 5.4 part8 :**

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

**Question 18 :**

Find the equation of the line passing through (22, -6) and having intercept on x-axis exceeds the intercept on y-axis by 5.

**Solution : **

**x-intercept(a) = b + 5, y -intercept = b **

**(x/a) + (y/b) = 1**

**x/(b+5) + y/b = 1**

**The straight line is passing through the point **(22, -6)

**22/(b+5) - 6/b = 1**

**22b - 6(b + 5) = b(b + 5)**

** 22b - 6b - 30 = b**²

** 16b - 30 = b**²

** b**²

** b**² - 11

**(b - 5) (b - 6) = 0**

b - 5 = 0 ==> b = 5 a = 5 + 5 = 10 ==> a = 10 x/a + y/b = 1 x/10 + y/5 = 1 (x + 2y)/10 = 1 x - 2y = 10 x + 2y - 10 = 0 |
b - 6 = 0 ==> b = 6 a = 6 + 5 = 11 ==> a = 11 x/a + y/b = 1 x/11 + y/6 = 1 (6x + 11y)/66 = 1 6x + 11y = 66 6x + 11y - 66 = 0 |

**Question 19 :**

If A (3, 6) and C (-1, 2) are two vertices of a rhombus ABCD, then find the equation of straight line that lies along the diagonal BD.

**Solution : **

In any rhombus diagonals bisect each other at right angle.

In any rhombus midpoint of the diagonals will be equal.

Midpoint of AC = Midpoint of BD

Midpoint of AC = (x₁+x₂)/2, (y₁+y₂)/2

= (3 + (-1))/2, (6 + 2)/2

= 2/2, 8/2

= (1, 4)

(1, 4) is a point lies of the diagonal BD.

Slope of AC x Slope of BD = -1

Slope of AC :

m = (y₂-y₁)/(x₂-x₁) ==> (2-6)/(-1-3) ==> -4/(-4) ==> 1

Slope of BD :

Slope of BD = -1/1 ==> -1

Equation of BD :

(y - y₁) = m (x - x₁)

y - 4 = -1(x - 1)

y - 4 = -x + 1

x + y - 4 - 1 = 0

x + y - 5 = 0

Hence the required equation is x + y - 5 = 0.

**Question 20 :**

Find the equation of the line whose gradient is 3/2 and which passes through P, where P divides the line segment joining A(-2, 6) and B (3, -4) in the ratio 2 : 3 internally.

**Solution :**

First we need to find the point P.

P = (lx₂ + mx₁)/(l + m), (ly₂ + my₁)/(l + m)

p = (2(3) + 3(-2))/(2+3), (2(-4) + 3(6))/(2+3)

= (6 -6)/5, (-8 + 18)/5

= 0/5, 10/5

= (0, 2)

(x₁, y₁) ==> (0, 2) m = 3/2

(y - y₁) = m(x - x₁)

(y - 2) = (3/2)(x - 0)

2(y - 2) = 3x

2y - 4 = 3x

3x - 2y + 4 = 0

Hence the required equation is 3x - 2y + 4 = 0.

After having gone through the stuff given above, we hope that the students would have understood "10th grade math solution exercise 5.4 part8".

Apart from the stuff given above, if you want to know more about "10th grade math solution exercise 5.4 part8", 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**