Coordinate Geometry - Study Mode

[#76] The straight line 2x + 3y = 12 passes through:
Correct Answer

(B) 1 st , 2 nd and 4 th quadrant

Explanation

Solution: $$eqalign{
& 2x + 3y = 12 cr
& Rightarrow frac{{2x}}{{12}} + frac{{3y}}{{12}} = 1 cr
& Rightarrow frac{x}{6} + frac{y}{4} = 1 cr} $$ ∴ Straight line 2x + 3y = 12, passes through 1 st , 2 nd and 4 th quadrant.

[#77] The area of a triangle with vertices A(0, 8), O(0, 0), and B(5, 0) is:
Correct Answer

(C) 20 sq. units

Explanation

Solution: On plotting the points on graph, $$ herefore { ext{Area of }}Delta = frac{1}{2} imes 5 imes 8 = 20{ ext{ sq}}{ ext{. units}}$$

[#78] In what ratio does the point T(x, 0) divide the segment joining the points S(-4, -1) and U(1, 4)?
Correct Answer

(A) 1 : 4

Explanation

Solution: $$eqalign{
& frac{{K,,,,,:,,,,,1}}{{Sleft( { - 4,, - 1}
ight),,,,,,,,,,Tleft( {x,,0}
ight),,,,,,,,,,Uleft( {1,,4}
ight)}} cr
& Rightarrow x = frac{{k{x_2} + {x_1}}}{{k + 1}},,,y = frac{{k{y_2} + {y_1}}}{{k + 1}} cr
& Rightarrow 0 = frac{{4k - 1}}{{k + 1}} Rightarrow x08oxed{k = frac{1}{4}} cr
& { ext{Ratio }}frac{1}{4}:1 = x08oxed{1:4} cr} $$

[#79] Point A (2, 1) divides segment BC in the ratio 2 : 3. Co-ordinates of B are (1, -3) and C are (4, y). What is the value of y?
Correct Answer

(D) 7

Explanation

Solution: $$eqalign{
& { ext{Now,}} cr
& Rightarrow 1 = frac{{2y - 9}}{5} cr
& Rightarrow 5 = 2y - 9 cr
& Rightarrow y = 7 cr} $$

[#80] The graphs of the equations 7x + 11y = 3 and 8x + y = 15 intersect at the point P, which also lies on the graph of the equation:
Correct Answer

(D) 3x + 5y = 1

Explanation

Solution: $$eqalign{
& 7x + 11y = 3,,,,*1 cr
& underline {,8x + y = 15,} ,,,,,underline {,*11,} cr
& ,,7x + 11y = 3 cr
& ,,88x + 11y = 165 cr
& underline {, - ,,,,,,,,, - ,,,,,,,,,, - ,,,,,,,,,,} cr
& - 81x = - 162 cr
& x = 2 cr
& y = 15 - 8 imes 2 cr
& y = - 1 cr} $$
Put value of x and y in options only option 'D' satisfy in this values 3x + 5y = 1 3 × 2 + 5 × (-1) = 1 6 - 5 = 1 = 1 [satisfied]